01 physics 5

IITJEE PHYSICS SAMPLE PAPER – IV
SECTION – I
Straight Objective Type
This section contains 8 multiple choice questions numbered 1 to 8. Each question has
4 choices (a), (b), (c) and (d), out of which ONLY ONE choice is correct.

1. A particle of mass m is projected at an angle of
60 with a velocity of 20 m/s relative to the
ground from a plank of same mass m which is
placed on a smooth surface initially plank was
at rest. The minimum length of the plank for
which the ball will fall on the plank itself is 0
(a) 40 3 m (b) 20 3 m =0
(c) 10 3 m (d) 60 3 m

2. A solid sphere of mass M and radius R is lying
on a rough horizontal plane. A constant force
F = 4 Mg acts vertically at point P such that OP
makes 60 with horizontal. Find the minimum
value of coefficient of friction so that sphere 60 
starts pure rolling
(a) 3/7 (b) 4/7
(c) 2/7 (d) 2/5

3. A sphere of mass m is rolling without sliding along positive x-axis on a rough horizontal
surface of coefficient of friction . It elastically collides with a wall and then returns back.
The correct statement of frictional force (f) acting on the sphere is
ˆ ˆ
(a) f = mg i before collision and f = – mg i after collision
ˆ
(b) f = 0 before collision and f = + mg i after collision
(c) f < ˆ
mg i before collision and f = ˆ
mg i just after collision

Space for rough work

(d) f = mg before collision and just after collision

4. One plate of a capacitor is connected to a spring as shown
in figure. 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 E
125 0 AE 2 4 0 AE 6 0E2 0AE 3
(a) (b) (c) (d)
32d 3 d2 Ad 3 2d3

5. All the rods are made of same material and have equal
cross-sectional area. Lengths of rods are such that L1 = L2 E
A
= L4 = L5 L3. Temperature A = B C 1 4
D E = F. D
C 3 40 
Consider the following statements for steady state. 1 50  2

(i) As 1 2, power through AC power through DF. 2 5 F
B
(ii) Power through CD = 2 (power through DF) which of
the following is correct?
(a) statement (i) is correct but (ii) is incorrect.
(b) statement (i) is incorrect but (ii) is correct
(c) both are incorrect
(d) both are correct.
dW
6. A certain mass of gas undergoes a process given by dU = . If the molar heat capacity of
2
15
the gas for this process is R, then the gas is
2
(a) monoatomic (b) polyatomic
(c) diatomic (d) data insufficient


7. A steel wire has a magnetic moment M. What will be its magnetic moment if it is bent into a
circular arc which is subtending angle 3 / 2 at the centre?
2 2M 2
(a) M (b) 2M/ (c) (d) M
3 3
8. de-Broglie wave in 5th Bohr orbit is
(a) (b)

(c) (d)

SECTION II
Reasoning Type
This section contains 4 reasoning type questions numbered 9 to 12. Each question contains
Statement-1 and Statement-2. Each question has 4 choices (a), (b), (c) and (d), out of which
ONLY ONE is correct.

Directions: Read the following questions and choose
(A) If both the statements are true and statement-2 is the correct explanation of
statement-1.
(B) If both the statements are true but statement-2 is not the correct explanation of
statement-1.
(C) If statement-1 is True and statement-2 is False.
(D) If statement-1 is False and statement-2 is True.

9. A solid sphere of copper of radius R and a hollow sphere of the same material of inner
radius r and outer radius R are heated to the same temperature and allowed to cool in the
same environment
Statement-1: Hollow sphere cools faster than solid sphere.
d 1
Statement-2:
dt m


(a) A (b) B (c) C (d) D
10. Statement-1: The principle of conservation of mechanical energy fails if there are non-
conservative forces doing work on the system.
Statement-2: Non-conservative forces, if work, result in change in mechanical energy
(a) A (b) B (c) C (d) D

11. In a rectilinear motion of a particle along x-axis velocity varies as v x where is a
positive constant. At t = 0, particle is located at origin.
Statement-1: The mean velocity of the particle averaged over the time that the particle
S
takes to cover the first S meters of the path is .
2
Statement-2: In a uniformly accelerated motion, the average velocity in a given duration is
the arithmetic mean of the velocities at the initial and final points of the given duration.
(a) A (b) B (c) C (d) D

12. Statement-1: The magnetic force experienced by a moving charged particle in a magnetic
field is invariant in nature just like any other force.
   
Statement-2: Magnetic force is F q v B and v is with respect to frame of reference in

which we are taking F .
(a) A (b) B (c) C (d) D
SECTION III
Linked Comprehension Type
This section contains 2 paragraphs P13 P18. Based upon each paragraph, 4 multiple choice
questions have to be answered. Each question has 4 choices (a), (b), (c) and (d), out of which
ONLY ONE choice is correct.

Passage-I
The task of the seatbelt is to stop you with the car so that your stopping distance is probably
4 or 5 times greater than if you had no seatbelt. A crash which stops the car and driver must
take away all its kinetic energy and the work energy principle then dictates that a longer
stopping distance decreases the impact force. For the example, in car crash scenario if the


stopping distance is d for a car moving with a speed v, the average force of impact can be
estimated by
Total work done = change in kinetic energy
1 2
Favgd = 0 - mv where m is the mass of the driver.
2
A moderate amount of stretch in the seatbelt will reduce the average impact force. A
moderate amount of stretch in a seatbelt harness can extend the stopping distance and
reduce the average impact force on the driver compared to a non-stretching harness. If the
belt is stretched by same length, it would reduce the deceleration by some amount. So
either a stretching or non stretching seatbelt reduces the impact force compared to no
seatbelt.
With no seat belt to stop the driver with the car, the driver flies free until stopped suddenly
by impact on the stearing column, windshield etc. The stopping distance is estimated to be
about one fifth of that with a seatbelt, causing the average impact force on the driver to be
five times as great. The work done to stop the driver is equal to the average impact force on
the driver times the distance travelled in stopping. A crash which stops the car and driver
must take away all its kinetic energy and the work energy principle then dictates that a
shorter stopping distance increases the impact force.
Answer the following questions in view of above passage:
For a car crash scenario, where a car stops in 30 cm from a speed of 54 kmph, what is the
force on the driver? Assume mass of the driver is 70 kg.

13. If the driver is firmly held in non stretching seat belt harness.
(a) 52500 N (b) 26250 N
(c) 13125 N (d) can’t be said

14. If the driver is not wearing a seatbelt and stopping distance is determined by nature of
collision with windshield, stearing column etc.
(a) 262500 N (b) 131250 N

15. If the driver is wearing a stretching seat belt harness (which increases the stopping distance
by 50 %)

(a) 35000 N (b) 17500 N
Passage-II
A point mass M is attached on the surface of a
sphere of same mass M and Radius R. this arrangement is
placed on a horizontal frictionless surface as shown in O
figure. (The line joining centre O of sphere to point mass M,R M
M is horizontal). If acm represents the acceleration of
centre of mass of the system (sphere + point mass ) and α
represents the angular acceleration of the system then
answer the following questions based upon the situation at
=0
the moment shown in figure

16. The magnitude of normal reaction from ground is
(a) equal to 2Mg (b) less than 2Mg (c) more than 2Mg (d) can’t determine
17. The correct relation between acm and α will be
(a) acm = √5/4 Rα (b) acm = 1/2 Rα (c) acm = Rα (d) None of these
18. If the ground is rough (instead of smooth), then the direction of friction force will be
(a) forward (b) backwards
(c) depend upon the value of µ (d) none of these
SECTION IV
Matrix Match Type
This section contains 2 questions. Each question contains statements given in two columns
which have to be matched. Statements (A), (B), (C), (D) in Column I have to be matched
with statements (1, 2, 3, 4) in Column II. One statement in first column has one or more than
one match with the statements in second column. The answers to these questions have to be
appropriately bubbled as illustrated in the following example.
If the correct matches are A 1,3, B 3, C 2,3 and D 2,4, then the correctly bubbled
4 × 4 matrix should be as follows:


1 2 3 4
A 1 2 3 4
B 1 2 3 4
C 1 2 3 4
D 1 2 3 4

1. Match the following
Column-I Column-II
(A) First law of thermodynamics 1. Conservation of kinetic energy
(B) Elastic collision 2. Conservation of energy
(C) Absence of dissipative force 3. Conservation of mass
(D) Equation of continuity 4. Conservation of mechanical energy
2. Match the following
Column-I Column-II
(A) An electron goes from A to B in a uniform
electric field.
e– E 1. Force decreases
A

B
(B) A bar magnet free to move in a uniform
magnetic field

B 2. K.E. increases
N
S
(C) A charge +q is projected away from the
centre of a charged ring along its axis
3. Force remains constant


+Q
+
+
+ m
+ +q v
++
(D) A particle executing SHM about O goes
from 2 to 1 (A and B are extreme points) 4. P.E. decreases
B A
2 1 O


SECTION V
Subjective or Numerical Type

The answer to these questions would lie between
0 to 9999. For any answer all four bubbles must be
filled, for example if you plan to answer as 16 then fill
0016 and if you plan to answer 0 then fill 0000 in the
grid provided in answer sheet. Any incomplete filling
will be considered as incorrect filling.
Illustration: If you want to fill 2379 as your answer
then it will be filled as

1. Two vessels A and B, thermally insulated, contain an ideal monoatomic gas. A small tube
fitted with a valve connects these vessels. Initially the vessel A has 2 litres of gas at 300 K
and 2 105 N/m2 pressure while vessel B has 4 litres of gas at 350 K and 4 105 N/m2
pressure. The valve is now opened and the system reaches equilibrium in pressure and
temperature. Calculate the new pressure and temperature.

2. A capacitor of capacity C1 = 2F is fully charged by using a cell of emf E = 4V. At an instant
t = 0, it is connected to an uncharged capacitor of capacity C2 = 3F through a resistance
x
R = 1 . If charge on the capacitor C2 grows with time t as 1 e 5t / 6 C, then find the
5
value of x.


01 physics 5

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