General Instructions:
(1)
There are 35 questions in all. All questions are compulsory
(2)
This question paper has five sections: Section A, Section B, Section C, Section
D and Section E. All the sections are compulsory.
(3)
Section A contains eighteen MCQ of 1 mark each, Section B contains seven
questions of two marks each, Section C contains five questions of three marks
each, section D contains three long questions of five marks each and Section E
contains two case study based questions of 4 marks each.
(4)
There is no overall choice. However, an internal choice has been provided in
section B, C, D and E. You have to attempt only one of the choices in such
questions.
5.
Use of calculators is not allowed.
SECTION A
1.
There are two Vernier Callipers both
of which have 1 cm divided into 10 equal divisions on the main scale as shown
in fig.
The measure values (in cm) by calliper C1
and C2, respectively are
a. 2.87
and 2.86
b. 2.85 and 2.82
C 2.87
and 2.87
d. 2.87 and 2.83
2.
The equation of state for a real gas
is given by
(P + a/V2)(V
– b) = RT
The dimensions of the constant ‘a’ are
a. [ML5T-2] b. [M-1L5T2]
C [ML-5T-1] d. [ML5T-1]
3.
A body starts from rest at time t =
0, the acceleration – time graph is shown in fig. The maximum velocity attained
by the body will be –
a. 110
m/s b. 55 m/s
C 650 m/s d. 550
m/s
4.
A car travels from A to B at a speed
of 20 Km/h and returns at a speed of 30 Km/h. The average speed of the car for
the whole journey is
a. 5
km/h
b. 24 km/h
C 25 km/h d. 50
km/h
5.
Which of the following statement is
false for a particle moving in a circle with a constant angular speed?
a. The
velocity vector is tangent to the circle.
b. The
acceleration vector is tangent to the circle.
c. The
acceleration vector points to the centre of the circle.
d. The
velocity and acceleration vectors are perpendiculars to each other.
6.
A displacement vector is a
a. Change
in position b.
Velocity
C Scalar d.
Distance without direction
7.
The angle between the two vectors
A = 3i + 4j + 5k and B = 3i
+ 4j – 5k will be
a. 900
b. 1800
C 00
d. 450
8.
A body of mass ‘m’ is placed on a
rough surface with coefficient of friction µ inclined at an angle ϴ. If the
mass is in equilibrium, then,
a. tanϴ
= µ
b. tanϴ = 1/µ
c tan ϴ = m/µ d. tanϴ =
µ/m
9.
A marble block of mass 2 kg lying on
ice when given a velocity of 6 m/s is stopped by friction in 10 sec. Then the
Coefficient of friction is
a. 0.01 b. 0.02
C 0.03
d. 0.06
10. A
man fires a bullet of mass 200 g at a speed of 5 m/s. The gun is of the one Kg
mass. By what velocity the gun rebounds backwards?
a. 1
m/s
b. 0.01 m/s
C
0.1 m/s d.
10 m/s
11. A
500 kg car takes a round turn of radius 50 m with a velocity of 36 Km/h. The
Centripetal force is
a. 1000
N
b. 750 N
C
250 N d. 1200 N
12. What
is F.S ?
a. Torque b.
Impulse
C. Momentum d.
Work
13. When a spring is
stretched by 2 cm, it stores 100 J of energy. If it is stretched further by 2
cm, the stored energy will be increased to
a. 100 J
b. 200 J
c. 300 J d. 400 J
14. A shell, in
flight, explodes into four unequal parts. Which of the following is conserved?
a. Potential energy b. Momentum
c. Kinetic Energy d. Both (a), (c)
15. Three identical
metal balls, each of the radius ‘r’ are placed touching each other on a
horizontal surface such that an equilateral triangle is formed when centres of
three balls are joined. The centre of the mass of the system is located at
a.
Line joining centres of any two balls
b. Centre of one of the balls.
c.
Horizontal surface
d.
Point of intersection of the medians.
16. An automobile
engine develops 100 Kw when rotating at a speed of 1800 rev/min. What torque
does it deliver?
a.
350 N.m b. 531
N.m
c.
440 N.m d. 628
N.m
17. In an elastic
collision,
a.
Both momentum and KE are conserved.
b.
Both momentum and KE are not conserved.
c.
Only energy is conserved.
d.
Only momentum is conserved
18. A particle is
moving in a circular path of radius ‘a’ under the action of an attractive
potential energy U = - K/(2r2). Its total energy is
a.
– K/(4a2) b. K/(2a2)
c. 0 d. – 3K/(2a2)
SECTION B
19. State and prove Work – Energy theorem for
constant force?
20. A circular race
track of radius 300 m is banked at an angle of 300. If the
coefficient of friction between the wheels and a race car and the road is 0.2,
What is the
a.
Optimum speed of the race car to avoid wear and tear on its tyres.
b.
Maximum permissible speed to avoid slipping?
21. A body is
projected with velocity of 40 m/s. After 2 seconds it crosses a vertical pole
of height 20.4 m. Calculate the angle of projection and horizontal range.
Or
Find
the centre of mass of a uniform L- shaped lamina ( a thin flat plate) with
dimensions as shown in fig. The mass of the lamina is 3 kg.
22. The
velocity- time graph of an object moving along a straight line as shown in fig.
Calculate
the distance covered by object between –
a. t
= 0 to t = 5 sec
b. t
= 0 to t = 10 sec
23. The
period of oscillation of simple pendulum is T = 2π(L/g)1/2. Measured
value of L is 20 cm known to 1 mm accuracy and time for 100 oscillations of the
pendulum is found to be 90 seconds using a wrist watch of 1 second resolution.
What is the accuracy in the determination of ‘g’?
Or
Find
the torque of a force 7i – 3j – 5k about the origin which acts on a particle
whose position vector is i + j – k.
24. A wooden block of
mass 2 kg rest on a soft horizontal floor. When an iron cylinder of mass 25 kg
is placed on the block, the floor yields steadily and the block and the
cylinder together go down with an acceleration of 0.1 m/s2. What is
the action of the block on the floor
a.
Before
b.
After the floor yields.
25. An insect trapped
in a circular groove of radius 12 cm, moves along the groove steadily and
completes 7 revolutions in 100 seconds.
a.
What is the angular speed and the linear speed of the motion?
b.
What is the magnitude of the acceleration.
SECTION C
26. The
frequency ‘υ’ of vibration of a stretched string depends upon-
1.
Its Length ‘l’
2.
Its mass per unit length ‘m’
3.
The tension T in the string.
Obtain
dimensionally an expression for the frequency ‘υ’.
27. As
soon as a car just starts from rest in a certain direction, a scooter moving
with a uniform speed overtakes the car. Their velocity – time graph are shown
in fig.
Calculate-
a. The
difference between the distances travelled by the car and the scooter in 15
seconds.
b. The
time when the car will catch up the scooter.
c. The
distance of car and scooter from the starting point at that instant.
28. Two
vectors A and B are inclined to each other at an angle ϴ. Using parallelogram law
of vector addition, find the magnitude and direction of their resultant.
Or
Show
that the centre of mass of a uniform rod of mass ‘M’ and length ‘L’ lies at the
middle point of the rod.
29. A
bullet of mass 0.01 kg is fired horizontally into a 4 kg wooden block at rest
on a horizontal surface. The coefficient of the kinetic friction between the
block and the surface is 0.25. The bullet gets embedded in the block and the
combination moves 20 m before coming to rest. With what speed did the bullet
strike the block?
Or
The
angular speed of a motor wheel is increased from 1200 rpm to 3120 rpm in 16
seconds.
a. What
is its angular acceleration, assuming the acceleration to be uniform.
b. How
many revolutions does the wheel make during this time?
30. In
the given fig. of motion in vertical circle having
radius
R, a spherical 
bob
of mass ‘m’ is connected at the
end
of the thread, it is observed that it is just able to
complete
the circle.
Calculate-
a. Velocity
at point A
b. Velocity
at point B
c. Velocity
at point C
SECTION D
31.
(1). Derive the relation for the final velocity of two
objects having masses m1 and m2 with initial velocity u1
and u2.
(2).
Two
balls bearings of mass ‘m’ each moving in opposite directions with equal speeds
‘v’ collide head on with each other. Predict the outcome of the collision
assuming it to be perfectly elastic.
Or
A ball moving on a
horizontal frictionless plane hits an identical ball at rest with a velocity of
0.5 m/s. If the collision is elastic, Calculate the speed imparted to the
target ball if the speed of the projectile after the collision is 30 cm/s. Show
that the two balls will move at right angles to each other after the collision.
32.
(1).
Write all three definitions of conservative forces?
(2).
What
do you mean by Inertia. Demonstrate it with the help of Galileo’s Experiment.
Or
A solid cylinder rolls
down an inclined plane. Its mass is 2 kg and radius 0.1 m. If the height of the
inclined plane is 4 m, What is its rotational Kinetic Energy when it reaches
the foot of the plane?
33.
A
body of mass 0.3 kg is taken up an inclined plane to length 10 m and height 5
m, and then allowed to slide down to the bottom again. The Coefficient of
friction between the body and the plane is 0.15. What is the-
a. Work done by the
gravitational force over the round trip.
b. Work done by the
applied force over the upward journey.
c. Work done by
frictional force over the round trip.
d. Kinetic energy of the
body at the end of the trip?
SECTION
E
34.
Case Study:
Read
the following paragraph and answer the question.
Newton’s
Second Law-
It states that the rate
of change of momentum of a body is directly proportional to the external force
applied on the body and the change takes place in the direction of the applied
force.
This law can be divided
into two parts:
1. The
rate of change of momentum is directly proportional to the applied force. The
larger the force acting on a body, greater is the change in its momentum.
2. The
Change of momentum occurs in the direction of the force.
Q1. Derive the relation F
= m.a
Q2. Is force a scalar or
vector quantity? Write its dimensional formula.
Q3. A car of mass 1000kg
is acted upon by a forward force of 1000 N due to engine and retarding force of
500 N due to friction. What will be the acceleration?
35.
Case Study:
Read
the following paragraph and answer the question.
Nature
of the work-
Positive
work- If a force acting on a body has a component in the
direction of the displacement, then the work done by the force is positive.
Negative
work- If a force acting on a body has a component in the
opposite direction of displacement, the work done is negative.
Zero
work- Work done by force is zero if the body gets diplaced
along a direction perpendicular to the direction of the applied force. Also,
the work done is zero if F or S or both are zero.
Q1. Write the dimensional
formula of work.
Q2. What is the SI unit
of the Work done?
Q3. What is the work done
by a person in carrying a suitcase weighing 10 kg f on his head when he travels
a distance of 5 m in the vertical direction? (take g=9.8 m/s2)
General Instructions:
(1)
There are 35 questions in all. All questions are compulsory
(2)
This question paper has five sections: Section A, Section B, Section C, Section
D and Section E. All the sections are compulsory.
(3)
Section A contains eighteen MCQ of 1 mark each, Section B contains seven
questions of two marks each, Section C contains five questions of three marks
each, section D contains three long questions of five marks each and Section E
contains two case study based questions of 4 marks each.
(4)
There is no overall choice. However, an internal choice has been provided in
section B, C, D and E. You have to attempt only one of the choices in such
questions.
5.
Use of calculators is not allowed.
SECTION A
1.
There are two Vernier Callipers both
of which have 1 cm divided into 10 equal divisions on the main scale as shown
in fig.
The measure values (in cm) by calliper C1
and C2, respectively are
a. 2.87
and 2.86
b. 2.85 and 2.82
C 2.87
and 2.87
d. 2.87 and 2.83
2.
The equation of state for a real gas
is given by
(P + a/V2)(V
– b) = RT
The dimensions of the constant ‘a’ are
a. [ML5T-2] b. [M-1L5T2]
C [ML-5T-1] d. [ML5T-1]
3.
A body starts from rest at time t =
0, the acceleration – time graph is shown in fig. The maximum velocity attained
by the body will be –
a. 110
m/s b. 55 m/s
C 650 m/s d. 550
m/s
4.
A car travels from A to B at a speed
of 20 Km/h and returns at a speed of 30 Km/h. The average speed of the car for
the whole journey is
a. 5
km/h
b. 24 km/h
C 25 km/h d. 50
km/h
5.
Which of the following statement is
false for a particle moving in a circle with a constant angular speed?
a. The
velocity vector is tangent to the circle.
b. The
acceleration vector is tangent to the circle.
c. The
acceleration vector points to the centre of the circle.
d. The
velocity and acceleration vectors are perpendiculars to each other.
6.
A displacement vector is a
a. Change
in position b.
Velocity
C Scalar d.
Distance without direction
7.
The angle between the two vectors
A = 3i + 4j + 5k and B = 3i
+ 4j – 5k will be
a. 900
b. 1800
C 00
d. 450
8.
A body of mass ‘m’ is placed on a
rough surface with coefficient of friction µ inclined at an angle ϴ. If the
mass is in equilibrium, then,
a. tanϴ
= µ
b. tanϴ = 1/µ
c tan ϴ = m/µ d. tanϴ =
µ/m
9.
A marble block of mass 2 kg lying on
ice when given a velocity of 6 m/s is stopped by friction in 10 sec. Then the
Coefficient of friction is
a. 0.01 b. 0.02
C 0.03
d. 0.06
10. A
man fires a bullet of mass 200 g at a speed of 5 m/s. The gun is of the one Kg
mass. By what velocity the gun rebounds backwards?
a. 1
m/s
b. 0.01 m/s
C
0.1 m/s d.
10 m/s
11. A
500 kg car takes a round turn of radius 50 m with a velocity of 36 Km/h. The
Centripetal force is
a. 1000
N
b. 750 N
C
250 N d. 1200 N
12. What
is F.S ?
a. Torque b.
Impulse
C. Momentum d.
Work
13. When a spring is
stretched by 2 cm, it stores 100 J of energy. If it is stretched further by 2
cm, the stored energy will be increased to
a. 100 J
b. 200 J
c. 300 J d. 400 J
14. A shell, in
flight, explodes into four unequal parts. Which of the following is conserved?
a. Potential energy b. Momentum
c. Kinetic Energy d. Both (a), (c)
15. Three identical
metal balls, each of the radius ‘r’ are placed touching each other on a
horizontal surface such that an equilateral triangle is formed when centres of
three balls are joined. The centre of the mass of the system is located at
a.
Line joining centres of any two balls
b. Centre of one of the balls.
c.
Horizontal surface
d.
Point of intersection of the medians.
16. An automobile
engine develops 100 Kw when rotating at a speed of 1800 rev/min. What torque
does it deliver?
a.
350 N.m b. 531
N.m
c.
440 N.m d. 628
N.m
17. In an elastic
collision,
a.
Both momentum and KE are conserved.
b.
Both momentum and KE are not conserved.
c.
Only energy is conserved.
d.
Only momentum is conserved
18. A particle is
moving in a circular path of radius ‘a’ under the action of an attractive
potential energy U = - K/(2r2). Its total energy is
a.
– K/(4a2) b. K/(2a2)
c. 0 d. – 3K/(2a2)
SECTION B
19. State and prove Work – Energy theorem for
constant force?
20. A circular race
track of radius 300 m is banked at an angle of 300. If the
coefficient of friction between the wheels and a race car and the road is 0.2,
What is the
a.
Optimum speed of the race car to avoid wear and tear on its tyres.
b.
Maximum permissible speed to avoid slipping?
21. A body is
projected with velocity of 40 m/s. After 2 seconds it crosses a vertical pole
of height 20.4 m. Calculate the angle of projection and horizontal range.
Or
Find
the centre of mass of a uniform L- shaped lamina ( a thin flat plate) with
dimensions as shown in fig. The mass of the lamina is 3 kg.
22. The
velocity- time graph of an object moving along a straight line as shown in fig.
Calculate
the distance covered by object between –
a. t
= 0 to t = 5 sec
b. t
= 0 to t = 10 sec
23. The
period of oscillation of simple pendulum is T = 2π(L/g)1/2. Measured
value of L is 20 cm known to 1 mm accuracy and time for 100 oscillations of the
pendulum is found to be 90 seconds using a wrist watch of 1 second resolution.
What is the accuracy in the determination of ‘g’?
Or
Find
the torque of a force 7i – 3j – 5k about the origin which acts on a particle
whose position vector is i + j – k.
24. A wooden block of
mass 2 kg rest on a soft horizontal floor. When an iron cylinder of mass 25 kg
is placed on the block, the floor yields steadily and the block and the
cylinder together go down with an acceleration of 0.1 m/s2. What is
the action of the block on the floor
a.
Before
b.
After the floor yields.
25. An insect trapped
in a circular groove of radius 12 cm, moves along the groove steadily and
completes 7 revolutions in 100 seconds.
a.
What is the angular speed and the linear speed of the motion?
b.
What is the magnitude of the acceleration.
SECTION C
26. The
frequency ‘υ’ of vibration of a stretched string depends upon-
1.
Its Length ‘l’
2.
Its mass per unit length ‘m’
3.
The tension T in the string.
Obtain
dimensionally an expression for the frequency ‘υ’.
27. As
soon as a car just starts from rest in a certain direction, a scooter moving
with a uniform speed overtakes the car. Their velocity – time graph are shown
in fig.
Calculate-
a. The
difference between the distances travelled by the car and the scooter in 15
seconds.
b. The
time when the car will catch up the scooter.
c. The
distance of car and scooter from the starting point at that instant.
28. Two
vectors A and B are inclined to each other at an angle ϴ. Using parallelogram law
of vector addition, find the magnitude and direction of their resultant.
Or
Show
that the centre of mass of a uniform rod of mass ‘M’ and length ‘L’ lies at the
middle point of the rod.
29. A
bullet of mass 0.01 kg is fired horizontally into a 4 kg wooden block at rest
on a horizontal surface. The coefficient of the kinetic friction between the
block and the surface is 0.25. The bullet gets embedded in the block and the
combination moves 20 m before coming to rest. With what speed did the bullet
strike the block?
Or
The
angular speed of a motor wheel is increased from 1200 rpm to 3120 rpm in 16
seconds.
a. What
is its angular acceleration, assuming the acceleration to be uniform.
b. How
many revolutions does the wheel make during this time?
30. In
the given fig. of motion in vertical circle having
radius
R, a spherical bob
of mass ‘m’ is connected at the
end
of the thread, it is observed that it is just able to
complete
the circle.
Calculate-
a. Velocity
at point A
b. Velocity
at point B
c. Velocity
at point C
SECTION D
31.
(1). Derive the relation for the final velocity of two
objects having masses m1 and m2 with initial velocity u1
and u2.
(2).
Two
balls bearings of mass ‘m’ each moving in opposite directions with equal speeds
‘v’ collide head on with each other. Predict the outcome of the collision
assuming it to be perfectly elastic.
Or
A ball moving on a
horizontal frictionless plane hits an identical ball at rest with a velocity of
0.5 m/s. If the collision is elastic, Calculate the speed imparted to the
target ball if the speed of the projectile after the collision is 30 cm/s. Show
that the two balls will move at right angles to each other after the collision.
32.
(1).
Write all three definitions of conservative forces?
(2).
What
do you mean by Inertia. Demonstrate it with the help of Galileo’s Experiment.
Or
A solid cylinder rolls
down an inclined plane. Its mass is 2 kg and radius 0.1 m. If the height of the
inclined plane is 4 m, What is its rotational Kinetic Energy when it reaches
the foot of the plane?
33.
A
body of mass 0.3 kg is taken up an inclined plane to length 10 m and height 5
m, and then allowed to slide down to the bottom again. The Coefficient of
friction between the body and the plane is 0.15. What is the-
a. Work done by the
gravitational force over the round trip.
b. Work done by the
applied force over the upward journey.
c. Work done by
frictional force over the round trip.
d. Kinetic energy of the
body at the end of the trip?
SECTION
E
34.
Case Study:
Read
the following paragraph and answer the question.
Newton’s
Second Law-
It states that the rate
of change of momentum of a body is directly proportional to the external force
applied on the body and the change takes place in the direction of the applied
force.
This law can be divided
into two parts:
1. The
rate of change of momentum is directly proportional to the applied force. The
larger the force acting on a body, greater is the change in its momentum.
2. The
Change of momentum occurs in the direction of the force.
Q1. Derive the relation F
= m.a
Q2. Is force a scalar or
vector quantity? Write its dimensional formula.
Q3. A car of mass 1000kg
is acted upon by a forward force of 1000 N due to engine and retarding force of
500 N due to friction. What will be the acceleration?
35.
Case Study:
Read
the following paragraph and answer the question.
Nature
of the work-
Positive
work- If a force acting on a body has a component in the
direction of the displacement, then the work done by the force is positive.
Negative
work- If a force acting on a body has a component in the
opposite direction of displacement, the work done is negative.
Zero
work- Work done by force is zero if the body gets diplaced
along a direction perpendicular to the direction of the applied force. Also,
the work done is zero if F or S or both are zero.
Q1. Write the dimensional
formula of work.
Q2. What is the SI unit
of the Work done?
Q3. What is the work done
by a person in carrying a suitcase weighing 10 kg f on his head when he travels
a distance of 5 m in the vertical direction? (take g=9.8 m/s2)
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