2. 1. What is perfectly elastic body? Give an example in which is close to
perfectly elastic.
2. Define modulus of elasticity. Name its three components.
3. Define the term strain. Why it has no units and dimensions? What are
different types of strain?
4. Define the term stress. Give its units and dimensions. Describe the
different types of stress.
5. On the basis of stress-strain curves, distinguish between ductile and
brittle materials.
6. (a) What is elastic potential energy?
(b) Derive an expression for the elastic potential energy stored in a stretched
wire under stress.
(c) Prove that elastic energy density is equal to ½ × stress × strain.
Mechanical Properties Of Solids
3. 7. (a) Define modulus of rigidity.
(b) A steel cable with a radius of 1.5cm supports a chairlift at a ski area. If the
maximum stress is not to exceed 108 n/m2, what is the maximum load, the
cable can support?
8. Two wires of diameter 0.25cm, one made of steel and the other of brass are
loaded as shown in figure. The unloaded length of steel wire is 1.5m and that
of brass wire is 1.0m. Compute the elongations of the steel and the brass wire.
4. 9. (a) Explain why should the beams used in the construction of bridges have
large depth and small breadth.
(b) Why are girders given I shape?
10. Explain the following terms:
(a) Ductile materials (b) Brittle material (c) Elastomers (d) Elastic after effect
(e) Elastic fatigue
Mechanical Properties Of Fluids
1. State and explain Pascal’s law of transmission of pressure. Name any two
applications of the principle
2. State the principle of a hydraulic lift and draw a neat diagram of it. What is the
value of its mechanical advantage?
3. (a) Why air bubbles in a liquid moves in upward direction?
(b)Why is it difficult to stop bleeding from a cut in human body at high altitudes?
(c)A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000
kg. The area of cross-section of the piston carrying the load is 425 cm2. What
maximum pressure would the smaller piston have to bear? [Ans. 6.92×105
N/m2]
5. 4. A U-tube contains water and methylated spirit separated by mercury. The
mercury columns in the two arms are in level with 10.0 cm of water in one arm
and 12.5 cm of spirit in the other. What is the specific gravity of the spirit?
[Ans. 0.8]
5. (a) Derive an expression for the pressure exerted by a liquid column of
height h.
(b) A column of water 40cm high supports a 30cm column of an unknown
liquid. What is the density of the liquid?
6. State and prove the equation of continuity for steady flow of an ideal fluid.
7. State and prove Bernoulli’s theorem. Give its limitation. Name any two
application of the principle.
8. State Torricelli’s law for efflux speed of a liquid and prove it.
9. Define terminal velocity. Write an expression for terminal velocity of a
sphere falling through a viscous liquid. Use the formula to explain the
observed rise of air bubbles in a liquid.
6. 10. Explain why:
(a) the angle of contact of mercury with glass is obtuse, while that of water
with glass is acute?
(b) the blood pressure in humans is greater at the feet than at the brain?
(c) hydrostatic pressure is a scalar quantity even though pressure is force
divided by area?
(d) a drop of liquid under no external forces is always spherical in shape?
a spinning cricket ball in air does not follow a parabolic trajectory?
(f) During a wind-storm, the roofs of the huts are blown off without damaging
the walls of the huts.
(g) When we try to close a water tap with our fingers, fast jets of water gush
through the openings between our fingers.
(h) Why still water run deep?
(i) We use a towel for getting our skin dry after taking bath.
(j) The antiseptic creams are generally prepared in petroleum jelly base.
(k) Why machines are sometimes jammed in extreme winter?
(l) How does (i) surface tension, (ii) viscosity of a liquid change on raising its
temperature?
7. (m) The hair of a paint brush cling together when the brush is taken out of paint
solution.
(n) The pressure on the concave side of a liquid is always greater than that on
its convex side?
(o) Does it matter if one uses gauge pressures instead of absolute pressures in
applying Bernoulli’s equation?
(p) the plane will lift on the basis of Bernoulli’s equation.
(q) to keep a piece of paper horizontal we should blow over, not under it.
(r) Water gushes out with high speed from tube of narrow cross-sectional area
11. Explain (a) Stokes Law (b) Newton’s Law of Viscosity.
12. Derive Ascent formula.
13. Derive Excess pressure in (a) in Liquid Drop (b) Soap Bubble
8. Thermal Properties Of Matter
1. Mass of 0.15kg of ice at 0°C is mixed with a 0.30kg of water at 50°C in a
container. Find the resultant temperature. Given the Latent heat of fusion of ice
= 3.35×105 J/kg and cwater = 4200 j kg_1 K-1.
2. Define (i) Specific heat capacity (ii) Heat capacity (iii) Molar specific heat
capacity at constant pressure and at constant volume and write their units.
3. What is meant by a black body. Explain how black body may be achieved in
practice. State and explain Stefan’s law?
4. Discuss energy distribution of a block body radiation spectrum and explain
Wein’s displacement law of radiation and Stefan’s law of heat radiation.
5. State Newton’s law of cooling. Derive mathematical expression for it.
6. The coefficient of volume expansion of glycerine is 49×10-5°C-1. What is the
fractional change in its density for a 30°C rise in temperature?
9. 6. Define (i) Specific heat capacity (ii) Heat capacity (iii) Molar specific heat capacity
at constant pressure and at constant volume and write their units
7. On what factors does the rate of heat conduction in a metallic rod in the steady
state depend. Write the necessary expression and hence define the coefficient
of thermal conductivity. Write its unit and dimensions.
8. What is Thermal Expansion? Derive the relation between Thermal Coefficient
Expansion.
Thermodynamics
1. What is a system said to be in the state of thermodynamic equilibrium?
2. Which of the following is not a path function?
10. 1. What is a system said to be in the state of thermodynamic equilibrium?
2. Which of the following is not a path function?
3. Define adiabatic process. Derive an expression for work done during adiabatic
process.
4. Write the conditions for a process to be (i) isothermal and (ii) adiabatic.
5. State first law of thermodynamics and express it mathematically. Apply first law
of thermodynamics to obtain the equation of state for an adiabatic process.
6. State first law of thermodynamics on its basis establish the relation between
two molar specific heat for a gas.
7. Why a gas has two principle specific heat capacities? What is the significance of
Cp - Cv and Cp / Cv where symbols have usual meaning.
11. 8. What is a cyclic process? Show that the net work done during a cyclic
process is numerically equal to the area of the loop representing the cycle.
9. On the basis of first law of thermodynamics show that in a cyclic process,
the total work done is equal to net amount of heat supplied to the system
during the complete cycle. State Kelvin-Planck’s statement of second law of
thermodynamics.
10. Explain why the air pressure in a car tyres increases during driving.
11. Heat is being supplied to a system but the system does not perform any
external work. Is it possible? If yes, how?
12. A thermodynamic system is taken from an original;
state to an intermediate state by the linear process shown
in figure.
13. Determine the PV relation for a monatomic gas undergoing
an adiabatic process.
12. 14. A geyser heats water flowing at the rate of 3.0 litres per minute from 27°C to
77°C. If the geyser operates on a gas burner, what is the rate of consumption of the
fuel if its heat of combustion is 4.0×104 J/g? [Ans. 15.75 g min-1]
15. Explain why:
(a) Two bodies at different temperature T1 and T2 (if brought in thermal contact do
not necessarily settle to mean temperature (T1 + T2)/2.
(b) The coolant in a chemical or a nuclear plant (i.e. the liquid used to prevent the
different parts of a plant from getting too hot) should have high specific heat.
(c) At pressure in a car tyres increases during driving.
(d) The climate of a harbour town in more temperate than that of a town in a desert
at the same latitude.
13. OSCILLATIONS
1. Can a motion be periodic but not oscillatory?
2. Can velocity and acceleration be in the same direction in a SHM?
3. What is phase relationship between displacement, velocity and acceleration in SHM?
4. The amplitude of a simple harmonic oscillator is doubled. How does this affect: (a)
the period (b) the total energy (c) the maximum velocity of the oscillator?
5.Write an expression for PE of a harmonic oscillator at any point.
6. The girl sitting on swing stands up. What will be the effect on periodic time of swing?
7. What will be the time period of a second pendulum inside an artificial satellite?
8. Deduce an expression for the (a) displacement (b) velocity (c) acceleration of a
particle executing SHM.
14. 9. The motion of a particle executing simple harmonic motion is described by the
displacement function, x = B sin (wt + a)
If the initial (t = 0) position of the particle is 1 cm and its initial velocity is
w cm/s, then what are its amplitude and initial phase angle? The angular
frequency of the particle is p rad s-1 .
10. A particle starts executing SHM from its positive extreme position. Draw graphs
showing variation of its potential energy, kinetic energy and the total energy with
time.
11. Derive the time period of simple Pendulum
12. Show that total mechanical energy of a particle executing simple harmonic motion
remains conserved with time, when dissipative forces are neglected.
15. Waves
1. Which of the following wave functions does not represent a travelling wave?
(a) y = (x – vt)2 (b) y = log(x +vt) (c) y = 1/x +vt (d) all of these
2. Solids can support both longitudinal and transverse waves, but only longitudinal
waves can propagate in gases. Give reason.
3. Define wavelength of a wave. Establish the relation u = vl for wave motion.
4. What do you understand by phase of a wave? How does the phase change with
time and position.
5. Discuss the Newton’s formula for velocity of sound in air. What correction was
applied to it by Laplace and why?
6. Why the speed of Sound in air (a) is independent of pressure, (b) increases with
temperature, (c) increase with humidity.
16. 7. Give the differences between progressive and stationary waves.
8. What are standing waves? Desire and expression for the standing waves. Also
define the terms node and antinode and obtain their positions.
9. What do you mean by node and antinode in a stationary wave? What is the
separation between them in terms of wavelength?
10. Show that frequencies of various harmonics set upon a vibrating string fixed at its
two ends are in the ratio of natural numbers.
11. What are beats? How are they produced. Briefly discuss the applications for this
phenomenon
12.
17. 13. What are standing waves? Desire and expression for the standing waves. Also
define the terms node and antinode and obtain their positions.
14. A steel wire has a length of 12.0m and a mass of 2.10kg. What should be the tension
in the wire so that speed of a transverse wave on the wire equals to the speed of sound
in dry air at 20°C = 343m/s.
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