For iit students

1. SECTION – I
Straight Objective Type
This section contains 9 multiple choice questions numbered 45 to 53. Each question has 4
choices (a), (b), (c), (d), out of which ONLY ONE is correct.
Q1. Two spheres of density ������1 and volume v are kept at distance d cm apart in a infinite
medium of density ������2(������2> ������1) with no other massive objects around.
Then the magnitude of net gravitational force on one sphere is given by
AG(������1 )2 ������ 2 /������2 where A is
(a) 1
(b) ������2 /������1
(c) (������2 -������1 )/������1
(d) (������2 - ������1 )/������2
Q2. Find the resultant of the wind forces on the fixed
advertising board shown in Fig. The intensity of wind force
normal to the board is 10 (1 + z) N/m2, where z is the
vertical distance from ground level.
(a) 120N
(b) 200N
(c) 480N
(d) 500N
Q3. There are three metallic cylinders of radius a, 2a and 3a and length l (length assumed to
be large in comparison to a). The cylinders are placed coaxially. Region between r=a and
r=2a is filled with dielectric of dielectric constant K=2. Find capacitance per unit length
of the system.
(a) (4∏Є0)/ (ln3-ln2) (c) (4∏Є 0)/ (ln3+2ln2)
(b) (8∏Є0)/ (2ln3-ln2) (d) (4∏Є0)/ (2ln3-ln2)
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2. Q4. Beats are heard when the A strings of two violins 1 & 2 are played together. The beat
frequency decreases as the tension in the A string of violin 1 is slowly increased. Which
statement is correct?
(a) The fundamental frequency of the A string in violin 1 is less than that for violin 2
(b) The fundamental frequency of the A string in violin 1 is greater than that for violin 2
(c) The fundamental frequency of the A string in violin 1 may be greater or less than
that violin 2
(d) None of these
Q5. The graph shown below in the figure represents energy Eλ versus ������ for three sources
sun, welding arc, tungsten filament. Correct Combination will be
(a) 1- Tungsten, 2- Welding Arc, 3- Sun
(b) 1- Sun, 2- Tungsten, 3- Welding Arc
(c) 1- Sun, 2 -Welding Arc, 3- Tungsten
(d) 1- Welding Arc, 2 - Sun, 3- Tungsten
Q6. An object is moving towards a converging lens on its axis. The image is also found to
be moving towards the lens. Then, the object distance ‘u’ must satisfy
(a) 2f<u<4f (b) f<u<2f (c) u>4f (d) u<f
Q7. A horizontal infinite slab of thickness 2a
extends from z=a to z=-a (see figure). It
carries a uniform current density (J=J������).
Then Magnetic field (B) is
(a) - µ0Ja Ĵ outside slab
(b) - µ0Ja|z|/z Ĵ outside slab
(c) - µ0Jaz2/a Ĵ outside slab
(d) - µ0Jz Ĵ outside slab
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3. Q8. A photon of energy 10.2 eV collides inelastically with a hydrogen atom in ground state.
After a certain time interval of few micro seconds another photon of energy 15.0 eV
collides inelastically with the same hydrogen atom, then the observation made by a
suitable detector is
(a) 1 photon with energy 10.2 eV and an electron with energy 1.4 eV.
(b) 2 photons with energy 10.2 eV.
(c) 2 photons with energy 1.4 eV.
(d) 1 photon with energy 3.4 eV and 1 electron with energy 1.4 eV.
More than one options correct:
Q1. Gate AB of negligible thickness shown in the figure below is 6m wide and weighs 50,000
kg when submerged. It is hinged at B and rests against a smooth wall at A. The correct
statements are….
(a) The water level h which will just cause the
gate to open is 4.5 m.
(b) If h = 4 m, the normal reaction on the
gate at point A is zero.
(c) If h = 4 m, the water to the left side of the
gate will apply a torque of 2000ρg.
(d) The net torque about B will be zero for all
values of h.
Q2. Two smooth spheres A & B of equal radii but of the masses 1 kg and 2 kg move with
speeds 21 m/s and 4 m/s respectively in opposite directions and collide. The velocity of
A is reduced to 1m/s in its original direction. Then, which of the following statements
is/are correct?
(a) The velocity of sphere B becomes 6 m/s and its direction is reversed
(b) The coefficient of restitution is 0.2
(c) The loss of kinetic energy of the system due to the collision is 200 J
(d) The magnitude of impulse applied by the two spheres on each other is 10 Ns
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4. Assertion- Reason Type Questions
A. Statement I and Statement II both are correct and Statement II is the reason for
Statement I.
B. Statement I and Statement II both are correct but Statement II is not the reason for
Statement I.
C. Statement I is false and Statement II is true.
D. Statement II is false and Statement I is true.
E. Both statements are false.
1. Statement1: If a point charge q is kept in front of an infinite grounded conducting
plane sheet, the electric field at any point in front of the sheet is only due to q,
whereas that on the other side of the sheet is zero.
Statement2: The region on the other side of the infinite grounded conducting plane
sheet is completely shielded from the influence of q
2. Statement1: Magnetic force field is not necessarily conservative.
Statement2: ������ . ������������ = μ0i which is not zero.
3. As the locks are opened, the ideal gas starts moving the steel piston against vacuum in
adiabatic chamber
Statement1: The temperature of the gas remains constant
Statement2: Work done by the gas is zero in adiabatic free expansion
4. Statement1: Two metallic spheres of same size, one of copper and the other of
aluminium, heated to the same temperature, will cool at the same rate when they are
suspended in the same enclosure.
Statement2: The rate of cooling of a body depends on the excess of temperature of
the body over the surroundings.
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5. Comprehension:
������ ×r
Q1.The magnetic field of a steady current is given by the Biot – Savart law : µ0 dl. The
4������������ 2
integration along the current path, in the direction of
flow. ������������ is an element along length of the wire and ������
is from source to a point P. The magnetic force on
segment of current carrying wire placed in a magnetic
field ������ is evidently ������ mag = ∫ (������ ×������ )������������ . The Magnetic
force on current carrying loop in uniform magnetic
field is zero. Net magnetic force on a curved wire say
PQR in uniform magnetic field is same as that in the
imaginary straight wire PR having same current as in
wire PQR.
1) Three wires of letters D,C,P having currents ( i1 = i2 = i3 )
as shown are placed in uniform magnetic field as
shown. Let F1 be the magnetic force due to
Magnetic Field ������ on letter D, F2 on C and F3 on P.
(a) F1 > F2 > F3 (b) F2 = F3 , F1 = 0
(b) F1 = 0 , F2 > F3 (d) F1 = 0 , F3 > F2
2) For what ratio of i2 & i1 The net force F2 = F3
������ ������
(a) 2 ������ = 1 (b) 2 ������ = 2
1 1
������1 ������1
(c) ������2 = 2 (d) ������2 = 3
3) If two wires of length L each carrying current i1 & i2 are
placed in uniform magnetic field. Find the magnitude of
net force permit length of wire 1. (assuming L to be
large)
������ 0 ������ 1������ 2
(a) Bi1 (b) Bi1 + 2������������
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6. ������ 0 ������ 1������ 2
(c) (d) none of these
2������������
1. A cylindrical vessel of height H=4m & area of cross section 1 m2 filled with water rests on a
stand of same height H. It has a small plugged hole of area of cross section ‘a’ near its
bottom. When plug is removed, the liquid starts to come out.
(1) The height of liquid as a function of time is
(a) h = ga2t2-4 2������at+8
1
(b) h = 2 ga2t2-4 2������at+4
1
(c) h = 2ga2t2-2 2������at+4
(d) h = ga2t2-2 2������at+8
(2) The range of the liquid as a function of instantaneous height of liquid in vessel is
(a) 2 ℎ (b) 4 ℎ (c) 2 2ℎ (d) 4 2ℎ
(3) The volume of the liquid collected in a large initially empty vessel lying on floor at a
distance H from the stand is
(a) 1m3 (b) 2 m3 (c) 3 m3 (d) 4 m3
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7. Match the columns:
Q1. In Young’s Double Slit
Experiment, Thin films (t1, μ1)
(t2, μ2) and t2>t1 are kept in
front of the slits in a medium of
refractive index μ. D is distance
between screen and slits. Then
match the following conditions
with the effect they will cause
on the diffraction pattern.
(a) μ2*t2≤ μ1*t1 (p) fringe width increases
(b) μ is increased (q) fringe width decreases
(c) (μ2-1)*t2= (μ1-1)*t1 (r) pattern shift upwards
(d) D is increased (s) pattern shift downwards
Q2. A spherical metallic conductor has a spherical cavity. A positive charge is placed inside
the cavity at its centre. Another positive charge is placed outside it. The conductor is
initially electrically neutral.
(a) If outside charge is shifted to other (p) Distribution of charge on inner surface
position of cavity changes
(b) If inside charge is shifted to other (q) Distribution of charge on outer surface
position within cavity of conductor changes
(r) Electric potential at center of
(c) If magnitude of charge inside cavity is conductor due to charges present
increased on outer surface of conductor
changes
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8. (s) Force on the charge placed inside the
(d) If conductor is earthed
cavity changes.
Q3. All the contact surfaces are frictionless. Then….
(a) (p) Net torque on the system about O is
zero
(b) (q) Angular momentum of the system
about O is not conserved
(c) (r) Impulsive normal reaction on the
system is provided from the ground.
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9. (s) Velocity of m does not change along
(d) common tangent
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