CBSE Class 11 Physics Systems Of Particles And Rotational Motion Worksheet

Question- A couple produces

(a) linear motion

(b) rotational motion

(c) both (a) and (b)

(d) neither (a) nor (b)

Answer-(b)

Question- Centre of mass of the earth and the moon system lies

(a) closer to the earth

(b) closer to the moon

(c) at the mid-point of line joining the earth and the moon

(d) cannot be predicted

Answer-(a)

Question- The motion of the centre of mass depends on

(a) total external forces

(b) total internal forces

(c) sum of (a) and (b)

(d) None of these

Answer-(a)

Question- In rotatory motion, linear velocities of all the particles of the body are

(a) same

(b) different

(c) zero

(d) cannot say

Answer-(b)

Question- The centre of mass of a rigid body lies

(a) inside the body

(b) outside the body

(c) neither (a) nor (b)

(d) either (a) or (b)

Answer-(d)

Question- Which of the following statements about angular momentum is correct?

(a) It is directly proportional to moment of inertia

(b) It is a scalar quantity

(c) both (a) and (b)

(d) None of these

Answer-(a)

Question- The centre of mass of two particles lies on the line

(a) joining the particles

(b) perpendicular to the line joining the particles

(c) at any angle to this line

(d) None of these

Answer-(a)

Question- If the resultant of all external forces is zero, then velocity of centre of mass will be

(a) zero

(b) constant

(c) either (a) or (b)

(d) neither (a) nor (b)

Answer-(c)

Question- The centre of mass of a body

(a) lies always outside the body

(b) may lie within, outside on the surface of the body

(c) lies always inside the body

(d) lies always on the surface of the body

Answer-(b)

Question- Which component of force contributes to the torque?

(a) Radial component

(b) Transverse component

(c) Both (a) and (b)

(d) Either radial or transverse

Answer-(b)

Question- The centre of mass of a body is the average position of its

(a) mass

(b) weight

(c) either mass or weight

(d) None of these

Answer-(a)

Question- The wide handle of screw is based upon

(a) Newton’s second law of motion

(b) law of conservation of linear momentum

(c) turning moment of force

(d) None of these

Answer-(c)

Question- The position of centre of mass of a system of particles does not depend upon the

(a) mass of particles

(b) symmetry of the body

(c) position of the particles

(d) relative distance between the particles

Answer-(d)

Question- The sum of moments of all the particles in a system about the centre of mass is always

(a) maximum

(b) minimum

(c) infinite

(d) zero

Answer-(d)

Question- The time rate of change of angular momentum of a particle is equal to

(a) force

(b) acceleration

(c) torque

(d) linear momentum

Answer-(c)

Question- According to the principle of conservation of angular momentum, if moment of inertia of a rotating body decreases, then its angular velocity

(a) decreases

(b) increases

(c) remains constant

(d) becomes zero

Answer-(b)

Question- Moment of inertia of a hollow cylinder of mass M and radius r about its own axis is

(a) 2 /3 Mr ²

(b) 2/ 5 Mr ²

(c) 1/3Mr ²

(d) Mr²

Answer-(d)

Question- The motion of a rigid body which is not pivoted or fixed in some way is either a pure ...A... or a combination of translation and rotation. The motion of a rigid body which is pivoted or fixed in some way is ...B... Here, A and B refer to

(a) rotation and translation

(b) translation and rotation

(c) translation and the combination of rotation and translation

(d) None of the above

Answer-(b)

Question-  Moment of inertia does not depend upon

(a) angular velocity of body

(b) shape and size

(c) mass

(d) position of axis of rotation

Answer-(a)

Question- The moment of inertia of a ...A... body about an axis ...B... to its plane is equal to the sum of its moments of inertia about two ...C... axes concurrent with perpendicular axis and lying in the plane of the body. Here, A, B and C refer to

(a) three dimensional, perpendicular and perpendicular

(b) planar, perpendicular and parallel

(c) planar, perpendicular and perpendicular

(d) three dimens

Answer-(c)

Question- Moment of inertia does not depend upon

(a) distribution of mass

(b) axis of rotation

(c) point of application of force

(d) None of these

Answer-(c)

Question- When a mass is rotating in a plane about a fixed point, its angular momentum is directed along the

(a) radius of orbit

(b) tangent to the orbit

(c) line parallel to plane of rotation

(d) line perpendicular to plane of rotation

Answer-(d)

Question- Rotational analogue of force in linear motion is

(a) weight

(b) angular momentum

(c) moment of inertia

(d) torque

Answer-(d)

Question- Force change the ...X... state of motion of a rigid body.

(a) Here X refers to rotational

(b) translational

(c) rotational and translational in general

(d) None of the above

Answer-(c)

Question- In rotation of a rigid body about a fixed axis, every ...A...of the body moves in a ...B..., which lies in a plane ...C... to the axis and has its centre on the axis. Here, A, B and C refer to

(a) particle, perpendicular and circle

(b) circle, particle and perpendicular

(c) particle, circle and perpendicular

(d) particle perpendicular and perpendicular

Answer-(c)

Question- Moment of inertia of a circular wire of mass M and radius R about its diameter is

(a) MR²/2

(b) MR²

(c) 2MR²

(d) MR²/4.

Answer-(a)

Question-  The moment of inertia of a uniform circular disc of radius ‘R’ and mass ‘M’ about an axis passing from the edge of the disc and normal to the disc is

(a) MR²

(b) 1/2 MR²

(c) 3/2 MR²

(d) 7/ 2 MR²

Answer-(c)

Question- During summersault, a swimmer bends his body to

(a) increase moment of Inertia

(b) decrease moment of Inertia

(c) decrease the angular momentum

(d) reduce the angular velocity

Answer-(b)

Question- Which of the following has the highest moment of inertia when each of them has the same mass and the same outer radius

(a) a ring about its axis, perpendicular to the plane of the ring

(b) a disc about its axis, perpendicular to the plane of the ring

(c) a solid sphere about one of its diameters

(d) a spherical shell about one of its diameters

Answer-(a)

Question-  A boy comes and sits suddenly on a circular rotating table.What will remain conserved for the table-boy system?

(a) Angular velocity

(b) Angular momentum

(c) Linear momentum

(d) Angular acceleration

Answer-(b)

Question- Radius of gyration of a body depends upon

(a) axis of rotation

(b) translational motion

(c) shape of the body

(d) area of the body

Answer-(a)

Question- Consider the following statements and select the correct statements.
I. The position of centre of mass depends upon the shape of the body
II. The position of centre of mass depends upon the distribution of mass
III. The positon of centre of mass is independent of the co-ordinate system chosen

(a) I and II only

(b) II and III only

(c) I and III only

(d) I, II and III

Answer-(d)

Question- For agiven mass and size, moment of inertia of a solid disc is

(a) more than that of a ring

(b) less than that of a ring

(c) equal to that of a ring

(d) depend on the material of ring and disc

Answer-(b)

Question- A circular disc A and a ring B have same mass and same radius. If they are rotated with the same angular speed about their own axis, then

(a) A has less moment of inertia than B

(b) A has less rotational kinetic energy than B

(c) A and B have the same angular momentum

(d) A has greater angular momentum than B

Answer-(a)

Question- The angular momentum of a system of particle is conserved

(a) when no external force acts upon the system

(b) when no external torque acts upon the system

(c) when no external impulse acts upon the system

(d) when axis of rotation remains same

Answer-(b)

Question- When a body starts to roll on an inclined plane, its potential energy is converted into

(a) translation kinetic energy only

(b) translation and rotational kinetic energy

(c) rotational energy only

(d) None of these

Answer-(b)

Question- A body cannot roll without slipping on a

(a) rough horizontal surface

(b) smooth horizontal surface

(c) rough inclined surface

(d) smooth inclined surface

Answer-(d)

Question- Choose the wrong statement from the following.

(a) The centre of mass of a uniform circular ring is at its geometric centre

(b) Moment of inertia is a scalar quantity

(c) Radius of gyration is a vector quantity

(d) For same mass and radius, the moment of inertia of a ring is twice that of a uniform disc

Answer-(b)

Question- A fan is moving around its axis, What will be its motion regarded as ?

(a) Pure rolling

(b) Rolling with shipping

(c) Skidding

(d) Pure rotation

Answer-(d)

Question- Analogue of mass in rotational motion is

(a) moment of inertia

(b) angular momentum

(c) torque

(d) None of these

Answer-(a)

Question- If a ring, a solid cylinder and a solid sphere roll down the same inclined plane without slipping then

(a) ring has the least velocity of centre of mass at the bottom of inclined plane

(b) sphere has the least velocity of centre of mass at the bottom of the inclined plane

(c) cylinder has the greatest velocity of centre of mass at the bottom of the inclined plane

(d) sphere has the least velocity of centre of mass at the bottom of the inclined plane

Answer-(a)

Question- If two circular discs A and B are of same mass but of radii r and 2r respectively, then the moment of inertia of A is

(a) the same as that of B

(b) twice that of B

(c) four times that of B

(d) 1/4 that of B

Answer-(d)

Question- Which of the following statements are incorrect about centre of mass?
I. Centre of mass can coincide with geometrical centre of a body
II. Centre of mass of a system of two particles does not always lie on the line joining the particles
III. Centre of mass should always lie on the body.

(a) II and III

(b) I and II

(c) I and III

(d) I, II and III

Answer-(a)

Question- A sphere rolls on a rough horizontal surface and stops. What does the force of friction do?

(a) It decreases the angular velocity

(b) It decreases the linear velocity

(c) It increases the angular velocity

(d) It decreases both angular and linear velocity

Answer-(c)

Question- Angular momentum of the particle rotating with a central force is constant due to

(a) constant torque

(b) constant force

(c) constant linear momentum

(d) zero torque

Answer-(d)

Question- Consider the following statements and choose the correct option.
I. Position vector of centre of mass of two particles of equal mass is equal to the position vector of either particle.
II. Centre of mass is always at the mid-point of the line joining two particles
III. Centre of mass of a body can lie where there is no mass

(a) I and II

(b) II only

(c) III only

(d) I, II and III

Answer-(c)

Question- Of the two eggs which have identical sizes, shapes and weights, one is raw, and other is half boiled. The ratio between the moment of inertia of the raw to the half boiled egg about central axis is

(a) one

(b) greater than one

(c) less than one

(d) not comparable

Answer-(b)

Question- Consider the following statements and select the correct option.
I. Moment of a couple depends on the point about which moment is taken.
II. Principle of moments holds only when parallel forces F1 and F2 are perpendicular to the lever
III. Centre of mass depends on the gravity
IV. Centre of mass depends on the distribution of mass of the body

(a) I and II

(b) III and IV

(c) I, II and III

(d) IV only

Answer-(d)

Question- Standing on a turn table, you are rotating holding weights in your hands outstretched horizontally, If you suddenly draw your hands and weights towards your chest, you will now

(a) stop rotating

(b) rotate as before

(c) rotate slower

(d) rotate faster

Answer-(d)

Question- Select the correct statement(s) from the following.
I. Moment of inertia is a scalar quantity
II. Angular acceleration requires torque
III. The rotational equivalent of distance is radius
IV. State of rest or motion of centre of mass can never be changed

(a) I only

(b) II only

(c) I and II

(d) II and IV

Answer-(b)

Question- A man standing on a rotating table is holding two masses at arm’s length. Without moving his arms, he drops the two masses. His angular speed will

(a) increase

(b) decrease

(d) become zero

(d) remain constant

Answer-(a)

Question- Two particles of mass m₁ and m₂ (m₁ > m₂) attract each other with a force inversely proportional to the square of the distance between them. If the particles are initially held at rest and then released, the centre of mass will

(a) move towards m₁

(b) move towards m₂

(c) remains at rest

(d) None of these

Answer-(c)

Question- A man stands at one end of a boat which is stationary in water. Neglect water resistance. The man now moves to the other end of the boat and again becomes stationary. The centre of mass of the ‘man plus boat’ system will remain stationary with respect to water

(a) in all cases

(b) only when the man is stationary initially and finally

(c) only if the man moves without acceleration on the boat

(d) only if the man and the boat have equal masses

Answer-(a)

Question- Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm. The distance of the centre of mass from the origin is

(a) 40 cm

(b) 45 cm

(c) 50 cm

(d) 30 cm

Answer-(a)

Question- Consider the following statements and select the correct statement(s).
I. Two satellites of equal masses orbiting the earth at different heights have equal moments of inertia
II. If earth were to shrink suddenly, length of the day will increase
III. Centre of gravity cannot coincide with centre of mass

(a) I only

(b) II only

(c) I and II

(d) I, II and III

Answer-(b)

Question- A planet is moving around the sun in an elliptical orbit. Its speed is

(a) same at all points of the orbit

(b) maximum when it is nearest to sun

(c) maximum when it is farthest from the sun

(d) cannot say

Answer-(b)

Question- A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α/ R form the centre of the bigger disc. The value of α is

(a) 1/4

(b) 1/3

(c) 1/2

(d) 1/6

Answer-(b)

Question- When sand is poured on a rotating disc, its angular velocity will

(a) decrease

(b) increase

(c) remain constant

(d) None of the above

Answer-(a)

Question- A disc is given a linear velocity on a rough horizontal surface then its angular momentum is

(a) conserved about COM only

(b) conserved about the point of contact only

(c) conserved about all the points

(d) not conserved about any point.

Answer-(b)

Question- Consider the following statements and select the correct statement(s).
I. Angular velocity is a scalar quantity
II. Linear velocity is a vector quantity
III. About a fixed axis, angular velocity has fixed direction
IV. Every point on a rigid rotating body has different angular velocity

(a) I only

(b) II only

(c) II and III

(d) III and IV

Answer-(c)

Question- A gymnast takes turns with her arms and legs stretched. When she pulls her arms and legs in

(a) the angular velocity decreases

(b) the moment of inertia decreases

(c) the angular velocity stays constant

(d) the angular momentum increases

Answer-(b)

Question- A shell following a parabolic path explodes somewhere in its flight. The centre of mass of fragments will continue to move in

(a) vertical direction

(b) any direction

(c) horizontal direction

(d) same parabolic path

Answer-(d)

Question. Moment of inertia does not depend upon
(a) distribution of mass
(b) axis of rotation
(c) point of application of force
(d) None of these

Answer: C

Question. A disc is given a linear velocity on a rough horizontal surface then its angular momentum is
(a) conserved about COM only
(b) conserved about the point of contact only
(c) conserved about all the points
(d) not conserved about any point.

Answer: B

Question. A body cannot roll without slipping on a
(a) rough horizontal surface
(b) smooth horizontal surface
(c) rough inclined surface
(d) smooth inclined surface

Answer: D

Question. A body is projected from ground with some angle to the horizontal. The angular momentum about the initial position will
(a) decrease
(b) increase
(c) remains same
(d) first increase then decrease

Answer: B

Question. A ball tied to a string is swung in a vertical circle. Which of the following remains constant?
(a) tension in the string
(b) speed of the ball
(c) centripetal force
(d) earth's pull on the ball

Answer: D

Question. Moment of inertia of a circular wire of mass M and radius R about its diameter is 
(a) MR²/2
(b) MR²
(c) 2MR²
(d) MR²/4.

Answer: A

Question. A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected ?
(a) Angular velocity
(b) Angular momentum
(c) Moment of inertia
(d) Rotational kinetic energy

Answer: B

Question. One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively IAand IB Such that 
(a) I_A < I_B
(b) I_A >I_B
(c) I_A = I_B
(d) I_A/I_B = d_A/d_B

Answer: A

Question. Angular momentum is
(a) moment of momentum
(b) product of mass and angular velocity
(c) product of M.I. and velocity
(d) moment of angular motion

Answer: A

Question. The angular momentum of a system of particle is conserved
(a) when no external force acts upon the system
(b) when no external torque acts upon the system
(c) when no external impulse acts upon the system
(d) when axis of rotation remains same

Answer: B

Question. Analogue of mass in rotational motion is
(a) moment of inertia
(b) angular momentum
(c) gyration
(d) None of these

Answer: A

Question. Moment of inertia does not depend upon
(a) angular velocity of body
(b) shape and size
(c) mass
(d) position of axis of rotation

Answer: A

Question. A hollow sphere is held suspended. Sand is now poured into it in stages.
(a) rises continuously
(b) remains unchanged in the process
(c) First rises and then falls to the original position
(d) First falls and then rises to the original position

Answer: D

Question. A particles performing uniform circular motion. Its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is
(a) L/4
(b) 2 L
(c) 4 L
(d) L/2

Answer: A

Question. A simple pendulum is vibrating with angular amplitude of 90° as shown in figure. 

For what value of θ is the acceleration directed
(i) vertically upwards
(ii) horizontally
(iii) vertically downwards 

Answer: A

Question. A solid sphere and a hollow sphere of the same material and of same size can be distinguished without weighing
(a) by determining their moments of inertia about their coaxial axes
(b) by rolling them simultaneously on an inclined plane
(c) by rotating them about a common axis of rotation
(d) by applying equal torque on them

Answer: B

Question. A stick of length L and mass M lies on a frictionless horizontal surface on which it is free to move in any way. A ball of mass m moving with speed v collides elastically with the stick as shown in fig.
If after the collision ball comes to rest, then what should be the mass of the ball?
(a) m = 2 M
(b) m = M
(c) m = M/2
(d) m = M/4

Answer: D

Question. Angular momentum of a system of a particles changes, when
(a) force acts on a body
(b) torque acts on a body
(c) direction of velocity changes
(d) None of these

Answer: B

Question. Five masses are placed in a plane as shown in figure. The coordinates of the centre of mass are nearest to 

(a) 1.2, 1.4
(b) 1.3, 1.1
(c) 1.1, 1.3
(d) 1.0, 1.0

Answer: C

Question. The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I0. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is
(a) I₀ + ML²/2
(b) I₀ + ML^2/4
(c) I₀ + 2ML²
(d) I0 + ML²

Answer: B

Question. A raw egg and a hard boiled egg are made to spin on a table with the same angular momentum about the same axis. The ratio of the time taken by the two to stop is
(a) = 1
(b) < 1
(c) > 1
(d) None of these

Answer: B

Question. A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad/s. The radius of the cylinder is 0.25 m. The K.E. associated with the rotation of the cylinder is
(a) 3025 J
(b) 3225 J
(c) 3250 J
(d) 3125 J

Answer: D

Question. What is the moment of inertia of a solid sphere of density r and radius R about its diameter? 

Answer: C

Question. A body having moment of inertia about its axis of rotation equal to 3 kg-m2 is rotating with angular velocity equal to 3 rad/s. Kinetic energy of this rotating body is the same as that of a body of mass 27 kg moving with a speed of
(a) 1.0 m/s
(b) 0.5 m/s
(c) 1.5 m/s
(d) 2.0 m/s

Answer: A

Question. The instantaneous angular position of a point on a rotating wheel is given by the equation q(t) = 2t³ – 6t². The torque on the wheel becomes zero at
(a) t = 1s
(b) t = 0.5 s
(c) t = 0.25 s
(d) t = 2s

Answer: A

Question. Centre of mass of the earth and the moon system lies
(a) closer to the earth
(b) closer to the moon
(c) at the mid-point of line joining the earth and the moon
(d) cannot be predicted

Answer: A

Question. A composite disc is to be made using equal masses of aluminium and iron so that it has as high a moment of inertia as possible. This is possible when
(a) the surfaces of the disc are made of iron with aluminium inside
(b) the whole of aluminium is kept in the core and the iron at the outer rim of the disc
(c) the whole of the iron is kept in the core and the aluminium at the outer rim of the disc
(d) the whole disc is made with thin alternate sheets of iron and aluminium

Answer: B

Question. A particle moves in a circle of radius 0.25 m at two revolutions per second. The acceleration of the particle in metre per second² is
(a) π²
(b) 8π²
(c) 4π²
(d) 2π²

Answer: C

Question. The radius of gyration of a body about an axis at a distance 6 cm from its centre of mass is 10 cm. Then, its radius of gyration about a parallel axis through its centre of mass will be
(a) 80 cm
(b) 8 cm
(c) 0.8 cm
(d) 80 m

Answer: B

Question. A particle of mass m is moving in a plane along a circular path of radius r. Its angular momentum about the axis of rotation is L. The centripetal force acting on the particle is
(a) L² /mr
(b) L² m/r
(c) L² /m r³
(d) L2 /m r²

Answer: C

Question. Two spheres A and B of masses m and 2m and radii 2R and R respectively are placed in contact as shown. The COM of the system lies 
(a) inside A
(b) inside B
(c) at the point of contact
(d) None of these

Answer: C

Question. The ratio of moment of inertia of circular ring & circular disc having the same mass & radii about on axis passing the c.m & perpendicular to plane is
(a) 1 : 1
(b) 2 : 1
(c) 1 : 2
(d) 4 : 1

Answer: B

Question. A rod of length L is pivoted at one end and is rotated with a uniform angular velocity in a horizontal plane. Let T₁and T₂ be the tensions at the points L/4 and 3L/4 away from the pivoted end. Then
(a) T₁ > T₂
(b) T₂ > T₁
(c) T₁ – T₂
(d) the relation between T₁ and T₂ depends on whether the rod rotates clockwise and anticlockwise.

Answer: A

Question. A particle of mass m is observed from an inertial frame of reference and is found to move in a circle of radius r with a uniform speed v. The centrifugal force on it is
(a) mv²/1 towards the centre
(b) mv²/1 away from the centre
(c) mv²/1 along the tangent through the particle
(d) zero

Answer: D

Question. Auniform rod of length l is free to rotate in a vertical plane about a fixed horizontal axis through O. The rod begins rotating from rest from its unstable equilibrium position.
When it has turned through an angle θ, its angular velocity ω is given as 

Answer: C

Question. A sphere of mass 2000 g and radius 5 cm is rotating at the rate of 300 rpm .Then the torque required to stop it in 2π revolutions, is
(a) 1.6 × 10² dyne cm
(b) 1.6 × 10³ dyne cm
(c) 2.5 × 10⁴ dyne cm
(d) 2.5 × 10⁵ dyne cm

Answer: D

Question. Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm. The distance of the centre of mass from the origin is
(a) 40 cm
(b) 45 cm
(c) 50 cm
(d) 30 cm

Answer: A

Question. Angular momentum is
(a) a polar vector
(b) an axial vector
(c) a scalar
(d) None of these

Answer: B

Question. A flywheel rotates about an axis. Due to friction at the axis, it experiences an angular retardation proportional to its angular velocity. If its angular velocity falls to half while it makes n rotations, how many more rotations will it make before coming to rest?
(a) 2n
(b) n
(c) n/2
(d) n/3

Answer: B

Question. A circular disc X of radius R is made from an iron plate of thickness t, and another disc Y of radius 4R is made from an iron plate of thickness t/4 . Then the relation between the moment of inertia IX and IY is
(a) Ι_Y = 32 Ι_X
(b) Ι_Y = 16 Ι_X
(c) Ι_Y = Ι_X
(d) Ι_Y = 64 ΙX

Answer: D

Question. A mass is tied to a string and rotated in a vertical circle, the minimum velocity of the body at the top is
(a) √gr
(b) g / r
(c) (g/r)^3/2
(d) gr

Answer: A

Question. A couple is acting on a two particle systems. The resultant motion will be
(a) purely rotational motion
(b) purely linear motion
(c) both a and b
(d) None of these

Answer: A

Question. Two particles A and B, initially at rest, moves towards each other under a mutual force of attraction. At the instant when the speed of A is v and the speed of B is 2 v, the speed of centre of mass is
(a) zero
(b) v
(c) 1.5 v
(d) 3 v

Answer: A

Question. If a running boy jumps on a rotating table, which of the following is conserved?
(a) Linear momentum
(b) K.E
(c) Angular momentum
(d) None of these

Answer: C

Question. A particle is confined to rotate in a circular path decreasing linear speed, then which of the following is correct?
(a) L̅ (angular momentum) is conserved about the centre
(b) only direction of angular momentum L̅ is conserved
(c) It spirals towards the centre
(d) its acceleration is towards the centre.

Answer: B

Question. A block Q of mass M is placed on a horizontal frictionless surface AB and a body P of mass m is released on its frictionless slope. As P slides by a length L on this slope of inclination q, the block Q would slide by a distance
(a) (m/M) L cos θ
(b) m L/(M + m)
(c) (M + m)/(m L cos θ)
(d) (m L cos θ) / (m + M)

Answer: D

Question. A small disc of radius 2 cm is cut from a disc of radius 6 cm.
If the distance between their centres is 3.2 cm, what is the shift in the centre of mass of the disc?
(a) 0.4 cm
(b) 2.4 cm
(c) 1.8 cm
(d) 1.2 cm

Answer: A

Question. Four particles of masses m₁,m₂,m₃ and m₄ are placed at the vertices A,B,C and D as respectively of a square shown.
The COM of the system will lie at diagonal AC if 
(a) m₁ = m₃
(b) m₂ = m₄
(c) m₁ = m₂
(d) m₃ = m₄

Answer: B

Question. If the linear density (mass per unit length) of a rod of length 3m is proportional to x, where x is the distance from one end of the rod, the distance of the centre of gravity of the rod from this end is
(a) 2.5 m
(b) 1 m
(c) 1.5 m
(d) 2 m

Answer: D

Question. A solid cylinder of mass m & radius R rolls down inclined plane without slipping. The speed of its C.M. when it reaches the bottom is
(a) √2gh
(b) √4gh / 3
(c) √3 / 4gh
(d) √4gh

Answer: B

Question. Point masses 1, 2, 3 and 4 kg are lying at the points (0, 0, 0), (2, 0, 0), (0, 3, 0) and (–2, –2, 0) respectively. The moment of inertia of this system about X-axis will be
(a) 43 kg –m²
(b) 34 kg–m²
(c) 27 kg – m²
(d) 72 kg – m²

Answer: A

Question. A mass m is moving with a constant velocity along a line parallel to the x-axis, away from the origin. Its angular momentum with respect to the origin
(a) is zero
(b) remains constant
(c) goes on increasing
(d) goes on decreasing.

Answer: B

Question. ABC is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. IAB, IBC and ICA are the moments of inertia of the plate about AB, BC and CA as axes respectively. Which one of the following relations is correct?
(a) IAB > IBC
(b) IBC > IAB
(c) IAB + IBC = ICA
(d) ICA is maximum

Answer: B

Question. A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be
(a) R²/K²+R²
(b) K²+R²/R²
(c) K²/R²
(d) K²/K²+R²

Answer: D

Question. A gymnast takes turns with her arms & legs stretched. When she pulls her arms & legs in
(a) the angular velocity decreases
(b) the moment of inertia decreases
(c) the angular velocity stays constant
(d) the angular momentum increases

Answer: B