The document is a sample physics test with multiple choice and numerical questions covering various physics topics. It contains 8 objective questions, 4 reasoning questions, and 2 passages with 4 questions each related to the passages. It also includes 2 matrix matching questions and 2 numerical/subjective questions requiring numeric answers. The test examines concepts in mechanics, thermodynamics, electromagnetism, and other core areas of physics.
The document provides information about a physics exam, including sample multiple choice questions and their explanations. Some key details:
- The exam contains two sections - one with single answer multiple choice questions, and one with multiple answer multiple choice questions.
- Sample questions cover topics like optics, mechanics, electromagnetism, and thermodynamics. The explanations show the conceptual steps and mathematical calculations used to arrive at the correct answers.
- Questions involve concepts like reflection, interference, momentum, work, harmonic motion, magnetic fields, electrostatics, and more. Diagrams are provided to illustrate some questions.
This document contains the chapter outline and answers to questions for a physics and measurement chapter. The chapter outline lists the main topics covered, including standards of length, mass and time, dimensional analysis, and significant figures. The answers to questions section provides worked solutions to sample problems related to these topics, such as density calculations, unit conversions, and dimensional analysis questions.
This document contains conceptual problems and questions about static equilibrium and elasticity. It includes the following:
1) True/false questions about the conditions for static equilibrium.
2) A question about the tension in different parts of a wire made of aluminum and steel.
3) Derivations of the expression for Young's modulus based on an atomic model and an estimate of the atomic force constant.
4) Questions involving calculating tensions, normal forces, and torque in situations involving objects in equilibrium, such as masts on sailboats and cylinders on steps.
5) Questions involving static equilibrium conditions to solve for quantities like the location of a person's center of gravity and the height a ladder can
(1) The document discusses fluid dynamics concepts including density, pressure, buoyancy, continuity, and Bernoulli's equation. It provides conceptual explanations and sample calculations for comparing volumes and densities of objects, calculating buoyant forces, and relating pressure, velocity, and flow rates in pipes.
(2) One example calculates the force needed to lift a car using a hydraulic lift, where the pressure applied must be the same at both the large and small pistons.
(3) Another example uses continuity and Bernoulli's equations to relate the velocity and pressure of water flowing at different diameters in a pipe. It finds the velocity and pressure change when the pipe narrows.
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
This document contains solutions to multiple problems involving slip-line field analysis. Problem 9-14 asks about a slip-line field for extrusion or drawing where r=0.0760 and α=15°. For extrusion, the stress σ2 at point 4,5 is found to be 1.842(2k). For drawing, σ2 would have the same magnitude but opposite sign. The product may depend on whether it is an extrusion or drawing, as extrusion would result in a thicker product while drawing a thinner product.
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
The document is a sample physics test with multiple choice and numerical questions covering various physics topics. It contains 8 objective questions, 4 reasoning questions, and 2 passages with 4 questions each related to the passages. It also includes 2 matrix matching questions and 2 numerical/subjective questions requiring numeric answers. The test examines concepts in mechanics, thermodynamics, electromagnetism, and other core areas of physics.
The document provides information about a physics exam, including sample multiple choice questions and their explanations. Some key details:
- The exam contains two sections - one with single answer multiple choice questions, and one with multiple answer multiple choice questions.
- Sample questions cover topics like optics, mechanics, electromagnetism, and thermodynamics. The explanations show the conceptual steps and mathematical calculations used to arrive at the correct answers.
- Questions involve concepts like reflection, interference, momentum, work, harmonic motion, magnetic fields, electrostatics, and more. Diagrams are provided to illustrate some questions.
This document contains the chapter outline and answers to questions for a physics and measurement chapter. The chapter outline lists the main topics covered, including standards of length, mass and time, dimensional analysis, and significant figures. The answers to questions section provides worked solutions to sample problems related to these topics, such as density calculations, unit conversions, and dimensional analysis questions.
This document contains conceptual problems and questions about static equilibrium and elasticity. It includes the following:
1) True/false questions about the conditions for static equilibrium.
2) A question about the tension in different parts of a wire made of aluminum and steel.
3) Derivations of the expression for Young's modulus based on an atomic model and an estimate of the atomic force constant.
4) Questions involving calculating tensions, normal forces, and torque in situations involving objects in equilibrium, such as masts on sailboats and cylinders on steps.
5) Questions involving static equilibrium conditions to solve for quantities like the location of a person's center of gravity and the height a ladder can
(1) The document discusses fluid dynamics concepts including density, pressure, buoyancy, continuity, and Bernoulli's equation. It provides conceptual explanations and sample calculations for comparing volumes and densities of objects, calculating buoyant forces, and relating pressure, velocity, and flow rates in pipes.
(2) One example calculates the force needed to lift a car using a hydraulic lift, where the pressure applied must be the same at both the large and small pistons.
(3) Another example uses continuity and Bernoulli's equations to relate the velocity and pressure of water flowing at different diameters in a pipe. It finds the velocity and pressure change when the pipe narrows.
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
This document contains solutions to multiple problems involving slip-line field analysis. Problem 9-14 asks about a slip-line field for extrusion or drawing where r=0.0760 and α=15°. For extrusion, the stress σ2 at point 4,5 is found to be 1.842(2k). For drawing, σ2 would have the same magnitude but opposite sign. The product may depend on whether it is an extrusion or drawing, as extrusion would result in a thicker product while drawing a thinner product.
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
This document provides solutions to problems involving the 1948 Hill yield criterion. It derives expressions for:
1) The angular variation of R as a function of stress components σx, σy, τxy using the Hill criterion and flow rules.
2) The ratio N/G in terms of R, P, and R45 using the results of the first problem.
3) Yield strengths Yθ at various angles θ by substituting values for N, F, G, and H into the Hill criterion equation.
The document provides solutions to problems involving determining stresses and strains in metal forming applications. Some key points:
1) It calculates principal stresses and strains for given stress/strain states.
2) It determines stresses in rods, tubes, and thin-walled pressure vessels under various loading conditions using stress/strain relationships.
3) It applies both Tresca and von Mises yield criteria to find yielding points for different materials under combinations of stresses.
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Kittel c. introduction to solid state physics 8 th edition - solution manualamnahnura
1. The document discusses crystallographic planes and directions in a cube, the Miller indices of planes with respect to primitive axes, and the spacing between dots projected onto different planes of a crystal structure.
2. Key concepts from crystallography such as Miller indices, primitive lattice vectors, reciprocal lattice vectors, and the first Brillouin zone are defined. Calculations of interplanar spacing and lattice parameters are shown for simple cubic and face-centered cubic lattices.
3. Binding energies, cohesive energies, and equilibrium properties are calculated and compared for body-centered cubic and face-centered cubic crystal structures. Approximations made in describing crystal binding using Madelung energies and pair potentials are
This document summarizes key information from Chapter 10 of an unknown text. It includes:
1) A nickel-base alloy billet split after the fourth pass of rolling with a 5% reduction per pass. Various experts proposed lowering the reduction, applying tension, or increasing the reduction.
2) The Mannesmann tube process involves small reductions between non-parallel rolls onto a flexible mandrel, creating low axial forces and keeping the mandrel centered.
3) Equations for deformation zone geometry reduce to simpler forms for small angles and reductions, with errors of around 2-5% for given values.
The document contains solutions to problems from Chapter 17-19 related to metal forming processes. It calculates pressures, strains, and radii required for tube expansion and hydroforming processes. It also analyzes stress states during hole expansion and describes the effect of aging times and temperatures on strain aging in low carbon steels.
This document discusses statically determinate and indeterminate beams. It introduces the concept of continuous beams, which have at least one hinged support and roller supports. The key equations for analyzing continuous beams are presented, including the three-moment equation. This equation relates the bending moments at the ends of adjacent beam segments and is used to solve for unknown support reactions and draw shear and moment diagrams. An example problem demonstrates applying the three-moment equation to determine reactions for a continuous beam with a single load.
This document contains solved problems related to electrostatics and dielectric materials. Key points include:
- The dielectric constant of a composite material is the weighted average of the dielectric constants of its constituent materials.
- Boundary conditions require the tangential electric field to be continuous across material interfaces, while the normal component is scaled by the relative permittivities of the materials.
- Energy density and stored electrostatic energy depend on the dielectric constant and electric field strength within each material.
- High dielectric constants and breakdown field strengths are desirable for capacitors to maximize the CVmax product.
Aiims previous year sample paper set 2Prabha Gupta
Find here previous year AIIMS question papers and solved sample question bank with answer keys at Aglasem. Visit @ https://admission.aglasem.com/aiims-mbbs-2019/
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
1. A particle moving perpendicular to a magnetic field will follow a circular path. The radius of the path is determined by the particle's mass, charge, speed, and the magnetic field strength.
2. A velocity selector uses uniform, perpendicular electric and magnetic fields. Particles pass through undeflected if their speed equals the ratio of the field strengths.
3. A mass spectrometer accelerates ions and uses a magnetic field to cause circular orbits. Heavier ions have smaller orbit radii allowing separation based on mass.
conceptual-problems-in-physics-for-iit-jee (1)APEX INSTITUTE
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems. We started to develop ways to enhance students IQ. We started to leave an indelible mark on the students who have undergone APEX training. That is why APEX INSTITUTE is very well known of its quality of education and the dedication towards its target.
1) A point charge moving through an electric field is shown to follow a parabolic trajectory given by z = -1.5×1010t2 m. At t = 3 μs, its position is found to be P(0.90, 0, -0.135) m.
2) A point charge moving through a uniform magnetic field follows a circular path. The equations of motion are derived and solved, giving the position, velocity, and kinetic energy at t = 3 μs.
3) Forces on current loops and filaments in various magnetic field configurations are calculated.
(Neamen)solution manual for semiconductor physics and devices 3edKadu Brito
This document contains solutions to problems from Chapter 1 of Semiconductor Physics and Devices: Basic Principles, 3rd edition. The problems calculate properties of semiconductor unit cells such as number of atoms, density, and volume percentage occupied by atoms. Lattice structures including simple cubic, body-centered cubic, face-centered cubic and diamond are considered. Properties of common semiconductors such as silicon and gallium arsenide are also calculated.
The document contains 10 problems involving electromagnetic induction and Maxwell's equations. Problem 10.1 involves calculating the voltage and current in a circuit with a changing magnetic flux. Problem 10.2 replaces a voltmeter with a resistor and calculates the resulting current. Problem 10.3 calculates the emf induced in closed paths with changing magnetic fluxes.
The document provides a summary of questions and answers from JEE(ADVANCED) – 2014 PAPER-2 Code-1. It includes 3 sections:
1) Section 1 contains 10 multiple choice questions with one correct answer each about physics concepts like kinetic energy, forces, electric fields, etc.
2) Section 2 contains 3 paragraphs with comprehension questions about thermodynamics, fluid dynamics, and electromagnetism.
3) Section 3 contains 4 matching questions pairing concepts from lists about physics problems involving charges, lenses, and inclined planes.
The summary briefly outlines the 3 main sections and types of questions contained in the document to provide the high-level structure and essential information.
This document contains a monthly physics test for Class XII with multiple choice and long answer questions. The test covers topics in electrostatics including electric field, electric flux, electric potential, electric dipole moment, Gauss's law, and Coulomb's law. It has 16 total marks worth of questions testing comprehension of fundamental concepts and abilities to define, derive and apply equations for various electrostatic situations.
1. The document provides a study guide for physics vocabulary review terms and concepts.
2. It contains fill-in-the-blank questions to test understanding of key physics terms like scientific method, dependent and independent variables, and significant digits.
3. The study guide also reviews SI units and how to determine the number of significant digits in measurements and calculations.
This study guide provides some tips for studying for the final exam, but does not contain everything needed. Students should use their chapter review worksheets, notes, and PowerPoints posted online to fully prepare. Key terms, concepts, and formulas are listed for several physics topics, along with questions to review. Students are advised to study these topics, practice problems from worksheets, and familiarize themselves with the provided formula sheet for the exam.
This physics study guide provides an overview of topics to review for an upcoming test, including motion, speed, velocity, acceleration, forces, and concepts from previous units. Students are instructed to review chapters 18-19 in their textbook, class notes, assignments, blogs, and homework. The guide includes 20 multiple choice and free response questions addressing these concepts to help students prepare.
This document provides solutions to problems involving the 1948 Hill yield criterion. It derives expressions for:
1) The angular variation of R as a function of stress components σx, σy, τxy using the Hill criterion and flow rules.
2) The ratio N/G in terms of R, P, and R45 using the results of the first problem.
3) Yield strengths Yθ at various angles θ by substituting values for N, F, G, and H into the Hill criterion equation.
The document provides solutions to problems involving determining stresses and strains in metal forming applications. Some key points:
1) It calculates principal stresses and strains for given stress/strain states.
2) It determines stresses in rods, tubes, and thin-walled pressure vessels under various loading conditions using stress/strain relationships.
3) It applies both Tresca and von Mises yield criteria to find yielding points for different materials under combinations of stresses.
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Kittel c. introduction to solid state physics 8 th edition - solution manualamnahnura
1. The document discusses crystallographic planes and directions in a cube, the Miller indices of planes with respect to primitive axes, and the spacing between dots projected onto different planes of a crystal structure.
2. Key concepts from crystallography such as Miller indices, primitive lattice vectors, reciprocal lattice vectors, and the first Brillouin zone are defined. Calculations of interplanar spacing and lattice parameters are shown for simple cubic and face-centered cubic lattices.
3. Binding energies, cohesive energies, and equilibrium properties are calculated and compared for body-centered cubic and face-centered cubic crystal structures. Approximations made in describing crystal binding using Madelung energies and pair potentials are
This document summarizes key information from Chapter 10 of an unknown text. It includes:
1) A nickel-base alloy billet split after the fourth pass of rolling with a 5% reduction per pass. Various experts proposed lowering the reduction, applying tension, or increasing the reduction.
2) The Mannesmann tube process involves small reductions between non-parallel rolls onto a flexible mandrel, creating low axial forces and keeping the mandrel centered.
3) Equations for deformation zone geometry reduce to simpler forms for small angles and reductions, with errors of around 2-5% for given values.
The document contains solutions to problems from Chapter 17-19 related to metal forming processes. It calculates pressures, strains, and radii required for tube expansion and hydroforming processes. It also analyzes stress states during hole expansion and describes the effect of aging times and temperatures on strain aging in low carbon steels.
This document discusses statically determinate and indeterminate beams. It introduces the concept of continuous beams, which have at least one hinged support and roller supports. The key equations for analyzing continuous beams are presented, including the three-moment equation. This equation relates the bending moments at the ends of adjacent beam segments and is used to solve for unknown support reactions and draw shear and moment diagrams. An example problem demonstrates applying the three-moment equation to determine reactions for a continuous beam with a single load.
This document contains solved problems related to electrostatics and dielectric materials. Key points include:
- The dielectric constant of a composite material is the weighted average of the dielectric constants of its constituent materials.
- Boundary conditions require the tangential electric field to be continuous across material interfaces, while the normal component is scaled by the relative permittivities of the materials.
- Energy density and stored electrostatic energy depend on the dielectric constant and electric field strength within each material.
- High dielectric constants and breakdown field strengths are desirable for capacitors to maximize the CVmax product.
Aiims previous year sample paper set 2Prabha Gupta
Find here previous year AIIMS question papers and solved sample question bank with answer keys at Aglasem. Visit @ https://admission.aglasem.com/aiims-mbbs-2019/
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
Dear Students/Parents
We at 'Apex Institute' are committed to provide our students best quality education with ethics. Moving in this direction, we have decided that unlike other expensive and 5star facility type institutes who are huge investors and advertisers, we shall not invest huge amount of money in advertisements. It shall rather be invested on the betterment, enhancement of quality and resources at our center.
We are just looking forward to have 'word-of-mouth' publicity instead. Because, there is only a satisfied student and his/her parents can judge an institute's quality and it's faculty members coaching.
Those coaching institutes, who are investing highly on advertisements, are actually, wasting their money on it, in a sense. Rather, the money should be invested on highly experienced faculty members and on teaching gears.
We all at 'Apex' are taking this initiative to improve the quality of education along-with each student's development and growth.
Committed to excellence...
With best wishes.
S . Iqbal
( Motivator & Mentor)
1. A particle moving perpendicular to a magnetic field will follow a circular path. The radius of the path is determined by the particle's mass, charge, speed, and the magnetic field strength.
2. A velocity selector uses uniform, perpendicular electric and magnetic fields. Particles pass through undeflected if their speed equals the ratio of the field strengths.
3. A mass spectrometer accelerates ions and uses a magnetic field to cause circular orbits. Heavier ions have smaller orbit radii allowing separation based on mass.
conceptual-problems-in-physics-for-iit-jee (1)APEX INSTITUTE
APEX INSTITUTE was conceptualized in May 2008, keeping in view the dreams of young students by the vision & toil of Er. Shahid Iqbal. We had a very humble beginning as an institute for IIT-JEE / Medical, with a vision to provide an ideal launch pad for serious JEE students . We actually started to make a difference in the way students think and approach problems. We started to develop ways to enhance students IQ. We started to leave an indelible mark on the students who have undergone APEX training. That is why APEX INSTITUTE is very well known of its quality of education and the dedication towards its target.
1) A point charge moving through an electric field is shown to follow a parabolic trajectory given by z = -1.5×1010t2 m. At t = 3 μs, its position is found to be P(0.90, 0, -0.135) m.
2) A point charge moving through a uniform magnetic field follows a circular path. The equations of motion are derived and solved, giving the position, velocity, and kinetic energy at t = 3 μs.
3) Forces on current loops and filaments in various magnetic field configurations are calculated.
(Neamen)solution manual for semiconductor physics and devices 3edKadu Brito
This document contains solutions to problems from Chapter 1 of Semiconductor Physics and Devices: Basic Principles, 3rd edition. The problems calculate properties of semiconductor unit cells such as number of atoms, density, and volume percentage occupied by atoms. Lattice structures including simple cubic, body-centered cubic, face-centered cubic and diamond are considered. Properties of common semiconductors such as silicon and gallium arsenide are also calculated.
The document contains 10 problems involving electromagnetic induction and Maxwell's equations. Problem 10.1 involves calculating the voltage and current in a circuit with a changing magnetic flux. Problem 10.2 replaces a voltmeter with a resistor and calculates the resulting current. Problem 10.3 calculates the emf induced in closed paths with changing magnetic fluxes.
The document provides a summary of questions and answers from JEE(ADVANCED) – 2014 PAPER-2 Code-1. It includes 3 sections:
1) Section 1 contains 10 multiple choice questions with one correct answer each about physics concepts like kinetic energy, forces, electric fields, etc.
2) Section 2 contains 3 paragraphs with comprehension questions about thermodynamics, fluid dynamics, and electromagnetism.
3) Section 3 contains 4 matching questions pairing concepts from lists about physics problems involving charges, lenses, and inclined planes.
The summary briefly outlines the 3 main sections and types of questions contained in the document to provide the high-level structure and essential information.
This document contains a monthly physics test for Class XII with multiple choice and long answer questions. The test covers topics in electrostatics including electric field, electric flux, electric potential, electric dipole moment, Gauss's law, and Coulomb's law. It has 16 total marks worth of questions testing comprehension of fundamental concepts and abilities to define, derive and apply equations for various electrostatic situations.
1. The document provides a study guide for physics vocabulary review terms and concepts.
2. It contains fill-in-the-blank questions to test understanding of key physics terms like scientific method, dependent and independent variables, and significant digits.
3. The study guide also reviews SI units and how to determine the number of significant digits in measurements and calculations.
This study guide provides some tips for studying for the final exam, but does not contain everything needed. Students should use their chapter review worksheets, notes, and PowerPoints posted online to fully prepare. Key terms, concepts, and formulas are listed for several physics topics, along with questions to review. Students are advised to study these topics, practice problems from worksheets, and familiarize themselves with the provided formula sheet for the exam.
This physics study guide provides an overview of topics to review for an upcoming test, including motion, speed, velocity, acceleration, forces, and concepts from previous units. Students are instructed to review chapters 18-19 in their textbook, class notes, assignments, blogs, and homework. The guide includes 20 multiple choice and free response questions addressing these concepts to help students prepare.
This document contains a physics test with multiple choice questions (Part A), reasoning questions (Part B), short answer questions (Part C), and long answer questions (Part D). The test covers topics in mechanics including motion, force, acceleration, momentum, friction, and Newton's laws of motion. It contains questions to calculate values like component forces, object acceleration, object momentum, and time for an object to fall.
Physics - Test on Measurement,Motion in one dimension and laws of motion,GRAD...tanushseshadri
Hey guys
Physics - Test on Measurement,Motion in one dimension and laws of motion
This doc is a test fr garde 9 ICSE students
If u like the document please do like it and follow me
TOPICS COVERED
MEASUREMENT
MOTION IN ONE DIMENSION
LAWS OF MOTION
This document provides an overview of key concepts in work, energy, and power. It includes definitions of work, kinetic energy, gravitational potential energy, elastic potential energy, and power. Sample problems demonstrate how to apply the concepts of work, energy, and conservation of mechanical energy to calculate quantities like speed and potential energy. Multiple choice and short response questions assess understanding of these physics topics.
Forces can be categorized into different types:
1) Gravity (Fg) is the force of attraction between objects with mass, directing objects on Earth downward.
2) Friction (Ff) resists the sliding of objects in contact and opposes their motion.
3) Air resistance (Ff) is a type of friction that opposes the motion of objects through the air.
4) Normal force (Fn) supports objects in contact with stable surfaces.
This document provides an overview of atomic structure and quantum mechanics concepts related to the atom. It discusses Rutherford scattering and the nuclear model of the atom, line spectra and the Bohr model of the hydrogen atom. It also covers de Broglie's explanation of Bohr's assumptions, the quantum mechanical picture including quantum numbers, and the Pauli exclusion principle and its relation to the periodic table. Key topics include atomic energy levels, wave-particle duality, allowed electron configurations, and how quantum mechanics improved on the limitations of older atomic models.
1. The document discusses reflection of light from plane and curved mirrors. It defines key terms used to describe reflection such as focal length, radius of curvature, and magnification.
2. Rules for image formation by curved mirrors are presented, including the location, size, and nature of the image for different positions of the object in front of concave and convex mirrors.
3. Examples with solutions are provided to illustrate concepts such as reflection angles, number of images formed by inclined mirrors, and speeds of moving mirrors and images.
#1. Physics B Exam - 1998 contains multiple choice questions about physics concepts tested on the AP Physics B Exam in 1998.
#2. The document contains 20 questions with basic ideas, solutions, and answers related to mechanics, electricity and magnetism, thermodynamics, and other physics topics.
#3. The questions cover a wide range of physics principles including kinematics, energy, momentum, electric fields, magnetic fields, waves, optics, and nuclear physics.
This presentation provides instructions for navigating a slideshow on vectors and projectile motion:
- To view as a slideshow, select "Slide Show" from the menu bar. Use arrow keys or space bar to advance.
- From the resources slide, click resources for their presentations.
- From the chapter menu, click lessons to go directly to them.
- Press Esc to exit the slideshow.
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Linear circuit analysis - solution manuel (R. A. DeCarlo and P. Lin) (z-lib.o...Ansal Valappil
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Physics Measurements Notes for JEE Main 2015 Ednexa
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12th Chemistry P-block elements Notes for JEE Main 2015 Ednexa
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Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
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The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
JEE Main Mock Test - Physics
1. Physics
Multiple Choice Questions
JEE Test-4
Q.1
A spherometer has 250 equal divisions marked along the periphery of its
disc, and one full rotation of the disc advances on the main scale by
0.0625 cm. The least count of the spherometer is
(a.1) 2.5 × 10-2 cm
(c.1) 2.5× 10-4 cm
#1#
(b.1) 25 × 10-3 cm
(d.1) none of the above
least count =
0.0625
cm = 2.5 × 10-4 cm
250
Q.2
From the top of a tower of height 40 m, a ball is projected with a speed
of 20 ms-1 at angle of elevation 30º. The ratio of the time taken by the
ball to come back to the same height and time taken to hit the ground is
(g=10ms-2)
(a.2) 2 : 1
(c.2) 4 : 1
#2#
(b.2) 1 : 2
(d.2) 1 : 4
The time taken to come back to the same height is
t1 =
2u sin q
=
2 ´ 20 ´ sin 30 °
g
= 2s
10
If t2 is the time taken to reach the ground, considering vertical downward
motion, we have
y = uy t2+
1
2
× g × t2
2
2. 40 = -(20 sin 30º) t2+
40 = -10
1
2
× 10 × t 2
2
t2+5 t 2
2
Or t 2 -2 t2 – 8 = 0
2
On solving t2 = 4s
t1
2
=
t2
Q.3
1
=
4
2
A particle moves in x – y plane according to equation x = 4t2+5t+16 and
6y = 5t The acceleration of the particle must be
(a.3) 8m/ sec2
(c.3) 12m/ sec2
#3#
(b.3) 14m/ sec2
(d.3) none of these
x = 4t2 + 5t + 16; y = 5t
dx
vx =
dt
dv x
ax =
= 8; ay =
dt
a =
Q.4
= 8t + 5 ; v y =
2
2
ax + ay =
dv y
dy
= 5
dt
= 0
dt
2
8 + 0 = 8m / s
2
A dynamometer D is attached to two bodies of masses M = 6 kg and
m=4kg. Forces F = 20 N and f = 10N are applied to the masses as
shown, The dyanometer reads
(a.4) 6 N
(c.4) 20 N
#4#
(b.4) 10 N
(d.4) 14 N
If a is acceleration of the system, then
a=
net force
total m ass
=
20 - 10
= 1ms
- 2
6+ 4
It is along the direction of
r
F
.
If R is reading of the dynamometer, then
R+Ma=F
R = F – Ma = 20 - 6 × 1 = 14 N
3. Q.5
Sand falls on to a conveyor belt at a constant rate of 2kg/s. If the belt is
moving at 0.1 m/s, then the extra force required to maintain speed of the
belt is
(a.5) 2N
(c.5) 0.2 N
#5#
(b.5) 20 N
(d.5) 10 N
dm
Here,
= 2 kg / s
dt
u=0.1 m/s
Extra force required = u ´
dm
=0.1× 2 = 0.2 N
dt
Q.6
A body of mass m is accelerated uniformly from rest to a speed ν in a
time T. The instantaneous power delivered to the body as a function of
time is given by
(a.6)
mv
T
(c.6)
#6#
2
2
1 mv
.t
(b.6)
2
T
2
2 T2
.t
(d.6)
2
Acceleration, a =
v
and F = m a =
T
2
mv
.t
2
1 mv
2
2 T2
.t
mv
T
Velocity acquired, V = at =
v
t
T
Instantaneous power,
P=FxV=
mv
T
Q.7
´
v
T
t=
mv
T
2
2
t
A rigid body rotates about a fixed axis with variable angular velocity
equal to (α-βt) at time t, where α and β are constants. The angle through
which it rotates before it comes to rest is
(a.7)
a
2
a
2
- b
2b
#7#
2
- b
2
a
(d.7)
a (a - b )
2b
(c.7)
2
(b.7)
2a
2
4. dq
w=
= a - bt
dt
d q = ( a - b t )d t
w h en w = 0, t =
a
b
q
t
ò d q = ò (a
q=
0
t
=
ò
0
t
a dt -
0
Q.8
- b t )d t
ò b td t
0
Select the proper graph between the gravitational potential (Vg) due to
hollow sphere and distance (r) from its centre.
(a.8)
(c.8)
#8#
(b.8)
(d.8)
Gravitational potential at a point outside the sphere V g =
- GM
r
But Vg is
same at a point inside the hollow sphere as on the surface of sphere.
Hence graph (c) is correct.
Q.9
A hollow steel pipe, with inner and outer diameter 8 cm and 10 cm
respectively and length 3 m support a roof. Its length increases by 0.1
mm due to load. The magnitude of load is (Y for steel is 2 × 1011Nm-2)
(a.9) 3.76 × 103N
(b.9) 188 N
(c.9) 37.6 N
(d.9) 1.88 × 104 N
5. #9#
F=
Y (A 2 - A 1 ) l
2
=
L
L
2 ´ 10
so F =
2
Y p (r2 - r1 ) l
11
2
2
´ (22 / 7 ) ´ (5 - 4 ) ´ 10
- 4
´ 10
- 4
3
4
= 1.88 ´ 10 N
Q.10 A large open tank has two holes in the wall. One is a square hole of side L
at a depth y from the top and the other is a circular hole of radius R at a
depth 4y from the top. When the tank is completely filled with water, the
quantities of water flowing out per second from both holes are the same.
Then R is equal to
(a.10) L
(c.10)
L/
(b.10) 2πL
(d.10) L/2π
2p
#10# Since volume is same in both cases AV = Constant
2
L ´
2
2gy = p R ´
or R = L /
2g ´ 4 y
2p
Q.11 In the P-V diagram shown in fig. ABC is a semicircle. The work done in
the process ABC is V(m3)
(a.11) zero
(b.11)
p
J
2
(c.11) 4J
(d.11) -
p
J
2
#11# In the part AB, volume of the gas is decreasing, and in the part BC,
volume of the gas is increasing. Therefore, WAB is negative and WBC is
positive. As |WBC| > |WAB|, therefore, net work done is positive.
Wnet = area of semicircle ABC =
1
2
2
pr =
1
2
2
p (1) =
p
2
joule
6. Q.12 Two gram of helium is enclosed in a vessel at NTP. How much heat
should be given to it to double the pressure. Specific heat of He is 3 J/gK.
(a.12) 800 J
(b.12) 819 J
(c.12) 1638 J
(d.12) 1600 J
#12# In vessel, volume is constant
∴ ∆Q = n CVdT
Now, n =
1
m ole
2
CV = 3×4=12 J/mole K
P2
At constant volume,
=
P1
T2
T1
To double the pressure, temp. of gas has to be doubled
i.e. if T1 = 273K
T2=546K
∴ ∆ T=T2-T1 = 546 – 273 = 273 K
From (i) ∆Q =
1
×12×273 = 1638 K.
2
Q.13 An electron tube was sealed off during manufacture at a pressure of 1.2
×10-7 mm of mercury at 27ºC. Its volume is 100 cm3. The number of
molecules that remain in the tube is (g=10m/s2)
(a.13) 3.86 ×1011
(b.13) 2 × 1016
(c.13) 3 × 1015
(d.13) 5 × 1011
#13# Here, P=1.2 × 10-7 mm of Hg
=1.2 × 10-7 × 10-3 × (13.6×103) ×10N/m2
Gas constant, R =
PV
=
(1.2 ´ 13.6 ´ 10
- 6
) ´ (100 ´ 10
- 6
)
300
T
= 1.2 × 13.6 × 10-12
N o. of m olecules =
6.023 ´ 10
23
´ 1.2 ´ 13.6 ´ 10
- 12
8.31
= 3.86 × 1011
Q.14 A string of mass 0.2 kg/m has length ℓ = 0.6m. It is fixed at both ends
and stretched such that it has a tension of 80 N. The string vibrates in
three segments with amplitude = 0.5 cm. The velocity of transverse wave
is
(a.14) 1.57 m/s
(b.14) 3.14 m/s
(c.14) 9.42 m/s
(d.14) 6.28 m/s
7. #14# As the string is vibrating in three segments, therefore,
l =
3l
i.e. l =
2l
2
=
3
T
As V =
V =
m
n=
V
l
=
2(0.6)
= 0.4 m
3
80
= 20 m / s
0.2
20
= 50 H z
0.4
ædy ö
A m plitude of particle velocity = ç ÷
= (a m ax ) w = a m ax (2 p n )
ç ÷
ç dt ÷
è øm ax
= (0.5 ´ 10
- 2
) ´ 2 p ´ 50 = 1.57 m / s
Q.15 One plate of a capacitor is connected to a spring as shown in fig. Area of
both the plates is A. In steady state, separation between the plates is 0.8
d (spring was unstretched and the distance between the plates was d
when the capacitor was uncharged). The force constant of the spring is
approximately
(a.15)
4 Î 0 AE
d
(c.15)
3
2 Î 0 AE
d
2
(b.15)
6Î 0 E
Ad
2
2
(d.15)
3
Î 0 AE
2d
2
3
3
#15# In equilibrium,
electrostatic force of attraction between the plates = restoring force in
the string
8. 2
q
2Î
= kx
A
0
(C E )
2Î
2
= k (d - 0.8d ) = 0.2 kd
A
0
2
C E
k=
2Î
A (0.2d )
0
N ow C =
2
Î
0
A
0.8d
Î
k=
2
0
A
0.64d
2
2
E
2Î
0
2
A (0.2d )
=
4Î
0
d
AE
2
3
Q.16 There are two concentric spheres of radius a and b respectively. If the
space between them is filled with medium of resistivity ρ, then the
resistance of the intergap between the two spheres will be
(a.16)
(c.16)
r æ1 1 ö
ç - ÷
÷
ç
è
ø
4p ç b a ÷
(b.16)
r æ1
1 ö
÷
ç
ç 2 - 2÷
÷
è
4p ç a
b ø
(d.16)
r
4 p (b + a )
r æ1 1 ö
÷
ç ÷
ç
è
ø
4p ç a
b÷
#16# Consider a concentric spherical shell of radius x and thickness dx as
shown in fig. Its resistance, dR is dR =
r dx
4p x
2
∴ Total resistance,
R =
r
4p
b
ò
a
dx
x
2
=
r é1 1 ù
ê ú
4 p êa
bú
ë
û
Q.17 An electron whose e/m is 1.76×1011 C/kg eneter a region where there is
a uniform magnetic field of induction 2 × 10-3 tesla with a velocity of
3 × 106 m/s in a direction making an angle of 45º with the field. The
pitch of its helical path in the region is
(a.17) 5.36 cm
(b.17) 8.4 cm
9. (c.17) 1.2 cm
(d.17) 3.8 cm
#17# When particle is projected at an angle θ other then 90º with the magnetic
field, the velocity of electron has two rectangular components (i) v sin θ
perpendicular to field (ii) v cos θ along the field. Here v sin θ provides
circular motion while v sin θ provides motion along the magnetic field.
Centripetal force,
m ( v sin q)
= Bq
r
i.e.
r
=
v sin q
m
Bq
2p r
T im e period , T =
=
2p m
v sin q
Bq
Pitch of helix,
h= v cos θ × T = v cos θ × 2πm / (Bq)
6
h=
3 ´ 10 ´ cos 45 ´ 2 ´ 3.14
11
1.76 ´ 10 ´ 2 ´ 10
- 3
h = 3.8 cm
u
r
$
k
Q.18 The magnetic field in a certain region is given by B = ( 4 0i - 1 8 $ ) g au ss .How
much flux passes through a 5.0 cm2 area loop in this region, if the loop
lies flat on the xy plane.
(a.18) 0
(b.18) 900 n Wb
(c.18) 9 Wb
(d.18) -900 n Wb
#18# As loop is in xy plane, only z component of magnetic field is effective
B=-18 gauss = -18 × 10-4 T
A = 5 × 10-4 m2
Φ = BA cos 0º = -18 × 10-4 × 5 ×10-4
= - 90 × 10-8 Wb=-900 × 10-9 Wb
=-900 n Wb
Q.19 In the circuit shown in fig. switch S is closed at time t = 0. The charge
which passes through the battery in one time constant is
10. EL
(a.19)
eR
(c.19)
(b.19)
2
eL
ER
2
æL ö
(d.19) E ç ÷
ç ÷
÷
eR E
çR ø
è
L
#19# In LR circuit, the growing current at time t is given by I=I0[1-e-t/τ]
E
Where I 0 =
L
and T =
R
R
∴ Charge passed through the battery in one time constant is
T
q=
T
ò Idt = ò I 0 (1 0
- t /T
) dt
0
éI e - t / T
q = I0 T - ê 0
ê
ê- 1 / T
ë
= I 0 T + I 0 T[e
- 1
= I0 T - I0 T +
q=
e
I0 T
ùT
ú
ú
ú0
û
- 1]
I0 T
e
(E / R )(L / R )
=
e
=
e
EL
eR
2
Q.20 If the time taken in exciting an electron is 10-2μs, then the uncertainty in
the frequency of emitted photon will be
(a.20) 1.6 × 105 Hz
(b.20) 1.6 × 107 Hz
(c.20) 1.6 × 109 Hz
(d.20) 1.6 × 1011 Hz
#20# As, ∆E=h∆ν and
DE =
h
h
=
Dt
2p D t
h
hD n =
2p D t
Dn =
1
2p D t
=
1
6.28 ´ 10
- 8
= 1.6 ´
7
10 H z
11. Q.21 Light of wavelength 6000Å is incident on a single slit. The first minimum
of the diffraction pattern is obtained at 4 mm from the centre. The screen
is at a distance of 2m from the slit. The slit width will be
(a.21) 0.15 mm
(b.21) 0.2 mm
(c.21) 0.3 mm
(d.21) 0.1 mm
#21# From a sin θ= nλ
a
x
= nl
a=
nl D
D
=
1´ 6000 ´ 10
4 ´ 10
x
- 10
´ 2
- 3
= 3 × 10-4 m = 0.3 mm
Q.22 The energy of a photon is equal to the kinetic energy of a proton. The
energy of a photon is E. Let λ1 be the de-Broglie wavelength of the
proton and λ2 be the wavelength of the photon. The ratio λ1/λ2 is
proportional to
(a.22) E0
(b.22) E-2
(c.22) E-1
(d.22) E1/2
#22#
For proton , E =
1
2
mn =
2
or p =
(m n )
2
=
2m
p
2
2m
2mE
D e - B roglie w avelength
l
1
=
h
=
p
l
1
l
h
2
=
2mE
h/
2mE
hc / E
=
E
2c
or
l
1
l
2
µ
E
Q.23 Radius of wavelength λ are incident on hydrogen atoms in the ground
state. A fraction of these radiations is absorbed by these atoms. There
are different wavelengths in the emission spectrum of excited atoms. One
of the values of λ will be
(a.23) 1211 Å
(b.23) 912 Å
(c.23) 950 Å
(d.23) 6208 Å
#23# No. of wavelengths in emission spectrum
12. n (n - 1)
N =
= 10
2
2
n - n - 20 = 0
n = 5 (- 4is not possible)
æ1
1
= Rç ç 2
2
ç1
l
è
5
1
25
l =
25
=
24 R
ö
÷ = 24 R
÷
÷
÷
25
ø
24 ´ 1.097 ´ 10
7
= 950 Å
Q.24 If a hydrogen atom at rest emits a photon of wavelength λ, the recoil
speed of the atom of mass m is
h
(a.24)
(b.24)
ml
l
(c.24)
mh
l
(d.24) mhλ
mH
#24# From de-Broglie wave equation,
l =
h
h
or p =
p
This is the momentum associated with photon emitted.
l
From the law of conservation of linear momentum, momentum of recoil
atom = p =
h
l
i.e.
mv =
h
l
v=
h
ml
Q.25 An AND gate
(a.25) is a universal gate
(b.25) is equivalent to a series switching circuit
(c.25) is impliments logic addition
(d.25) is equivalent to a parallel switching circuit.
#25# For AND gate; we get output only if A = 1 and B = 1 i.e. AND gate is
equivalent to a series switching circuit.
Q.26 The value of current in the following diagram will be
13. (a.26) 10 amp
(b.26) 10-2 amp
(c.26) 0 amp
(d.26) 0.025 amp
#26# Here p-n junction is forward biased with voltage
= 5 – 3 = 2V.
∴ current I =
2
1
=
200
= 10
- 2
A
100
Q.27 The carrier frequency generated by a tank circuit containing 1 nF
capacitor and 10 microhentry inductor is
(a.27) 159.2 Hz
(b.27) 1592 Hz
(c.27) 1592 kHz
(d.27) 15920 Hz
#27# C=1nF = 10-9 F, L=10μH = 10-5 H
1
n=
2p
1
=
LC
2 p 10
- 5
=
´ 10
- 9
10
7
2p
= 1.592 × 106 Hz = 1592 kHZ
Q.28 A travelling microscope focused directly on an ink dot reads 2.758cm. A
glass slab is placed on the dot. The microscope is focused on the dot and
its scale reading is 3.398 cm. The microscope is now focused on the
surface of the glass slab and it reads 4.680 cm. What is refractive index
of material of the slab?
(a.28) 1.5
(b.28) 3.398
(c.28) 1.6
(d.28) 2.758
#28# Here, position of object O : R1 = 2.758cm
Position of image I : R2 = 3.398 cm
Position of top surface, S ; R3 = 4.680 cm
m=
real depth (O S)
apparent depth (IS)
=
R 3 - R1
=
R3 - R2
=
1.922
4.680 - 2.758
4.680 - 3.398
= 1.5
1.282
Q.29 Two liquids are at temps. 20ºC and 40ºC. When same mass of both of
them is mixed, the temperature of the mixture is 32ºC. What is the ratio
of their specific heats ?
(a.29) 3/2
(b.29) 1/3
(c.29) 2/3
(d.29) 2/5
14. #29# Heat gained by one = Heat lost by the other
C1 × m (32-20) = C2 × m (40-32)
C1
8
=
C2
=
12
2
3
Q.30 For a given sonometer wire under given tension, first resonance length
with a fork of frequency 256 is 20 cm. If fork of frequency 512 is used,
the first resonance length would be
(a.30) 20 cm
(b.30) 10 cm
(c.30) 40 cm
(d.30) 30 cm
#30#
As
n1
=
l2
l1
=
l2
20
n2
256
512
l2 =
256´ 20
512
= 1 0 cm