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Rotational Dynamics MCQs for Students
Analogue of mass in rotational motion is
(a) moment of inertia
(b) angular momentum
(c) gyration
(d) None of these
Option a – moment of inertia
The moment of inertia does not depend upon
(a) angular velocity of the body
(b) shape and size
(c) mass
(d) position of the axis of rotation
Option a – angular velocity of the body
During a summersault, a swimmer bends his body to
(a) increase the moment of Inertia
(b) decrease the moment of Inertia
(c) decrease the angular momentum
(d) reduce the angular velocity
Option b – decrease the moment of Inertia
Of the two eggs which have identical sizes, shapes and weights, one is raw, and the other is half-boiled. The ratio between the moment of inertia of the raw to the half-boiled egg about a central axis is
(a) one
(b) greater than one
(c) less than one
(d) not comparable
Option b – greater than one
A mass is resolving in a circle which is in the plane of the paper. The direction of angular acceleration is
(a) upward the radius
(b) towards the radius
(c) tangential
(d) at a right angle to angular velocity
Option a – upward the radius
A solid sphere is rotating in free space. If the radius of the sphere is increased keeping the 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
Option b – Angular momentum
Angular momentum is
(a) the moment of momentum
(b) the product of mass and angular velocity
(c) the product of M.I. and velocity
(d) the moment of angular motion
Option a – the moment of momentum
The angular momentum of a system of particles 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 the axis of the rotation remains the same
Option b – when no external torque acts upon the system
A couple is acting on 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
Option a – purely rotational motion
The angular momentum of a system of particles changes, when
(a) the force acts on a body
(b) torque acts on a body
(c) the direction of velocity changes
(d) None of these
Option b – torque acts on a body
A body rolls down an inclined plane. If its K.E. of rotational motion is 40% of its K.E. of translational, then the body is a
(a) cylinder
(b) ring
(c) solid disc
(d) solid sphere
Option d – solid sphere
The relation between torque and angular momentum is similar to the relation between
(a) energy and displacement
(b) acceleration and velocity
(c) mass and moment of inertia
(d) force and linear momentum
Option d – force and linear momentum
For which one of the following does the centre of mass lie outside the body?
(a) A fountain pen
(b) A cricket ball
(c) A ring
(d) A book
Option c – A ring
A ring of mass m and radius r is melted and then moulded into a sphere. The moment of inertia of the sphere will be
(a) more than that of the ring
(b) less than that of the ring
(c) equal to that of the ring
(d) None of these
Option b – less than that of the ring
One solid sphere and disc of the same radius are falling along an inclined plane without slipping. One reaches earlier than the other due to
(a) the different radii of gyration
(b) different sizes
(c) different friction
(d) different moments of inertia
Option a – the different radii of gyration
A solid sphere, disc and solid cylinder all of the same mass and made of the same material are allowed to roll down (from rest) on an inclined plane, then
(a) the solid sphere reaches the bottom first
(b) the solid sphere reaches the bottom last
(c) the disc will reach the bottom first
(d) all reach the bottom at the same time
Option a – the solid sphere reaches the bottom first
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 the plane of rotation
(d) a line perpendicular to the plane of rotation
Option d – a line perpendicular to the plane of rotation
A body cannot roll without slipping on an ( Rotational Dynamics MCQs )
(a) rough horizontal surface
(b) smooth horizontal surface
(c) rough inclined surface
(d) smooth inclined surface
Option d – smooth inclined surface
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
Option b – translation and rotational kinetic energy
If a running boy jumps on a rotating table, which of the following is conserved?
(a) Linear momentum
(b) Kinetic energy
(c) Angular momentum
(d) None of these
Option c – Angular momentum
If a particle is confined to rotate in a circular path with decreasing linear speed, then which of the following is correct?
(a) L (angular momentum) is conserved about the centre
(b) only the direction of angular momentum L is conserved
(c) It spirals towards the centre
(d) its acceleration is towards the centre.
Option b – only direction of angular momentum L is conserved
Two particles A and B, initially at rest, move 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 the centre of mass is
(a) zero
(b) v
(c) 1.5 v
(d) 3 v
Option a – zero
A ball balanced on a vertical rod is an example of ( Rotational dynamics mcqs )
(a) stable equilibrium
(b) unstable equilibrium
(c) neutral equilibrium
(d) perfect equilibrium
Option b – unstable equilibrium
There are some passengers inside a stationary railway compartment. The centre of mass of the compartment itself (without the passengers) is C₁, while the centre of mass of the ‘compartment plus passengers’ system is C₂. If the passengers move about inside the compartment then
(a) both C1 and C2 will move with respect to the ground
(b) neither C₁ nor C2 will be stationary with respect to the ground
(c) C₁ will move but C2 will be stationary with respect to the ground
(d) C₂ will move but C1 will be stationary with respect to the ground
Option c – C₁ will move but C2 will be stationary with respect to the ground
Let I1 and I2 be the moments of inertia of two bodies of identical geometrical shapes, the first made of aluminium and the second of iron. Then
(a) I₁ > I₂
(b) I₁ = I₂
(c) I₁ < I₂
(d) relation between I1 and I2 depends on the actual shapes of the bodies
Option c – I₁
A man hangs from a rope attached to a hot-air balloon. The mass of the man is greater than the mass of the balloon and its contents. The system is stationary in the air. If the man now climbs up to the balloon using the rope, the centre of mass of the ‘man plus balloon system will
(a) remain stationary
(b) move up
(c) move down
(d) first, move up and then return to its initial position
Option a – remain stationary
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.
Option b – remains constant
A raw egg and a hard-boiled made 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
Option b –
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 the 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
Option b – the whole of the aluminium is kept in the core and the iron at the outer rim of the disc
A solid cylinder and a hollow cylinder both of the same mass and the same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?
(a) Solid cylinder
(b) Both together
(c) One with a higher density
(d) Hollow cylinder
Option a – Solid cylinder
A man stands at one end of a boat which is stationary in the 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
Option a – in all cases
Mechanical advantage is a concept based on ( Rotational dynamics mcqs )
(A) moment of inertia
(B) principle of moments
(C) equilibrium of the rigid body
(D) parallel axis theorem
Option b – principle of moments
The statement; the angular acceleration is directly proportional to the applied torque and is inversely proportional to the moment of inertia of the body, can be called
(A) Newton’s second law of motion for rotating bodies.
(B) Newton’s second law of motion for a body rotating along the axis passing through its center.
(C) Newton’s second law of motion for a body rotating about a fixed axis.
(D) Newton’s second law of motion for a body rotating about an axis perpendicular to the plane of the body.
Option c – Newton’s second law of motion for a body rotating about a fixed axis.
A toy car placed on a rough table possesses
(A) no equilibrium
(B) translational equilibrium
(C) rotational equilibrium
(D) translational and rotational equilibrium
Option d – translational and rotational equilibrium
The total torque on a system is
(A) independent of origin.
(B) independent of origin if the total external force acting is zero.
(C) independent of origin if the total external force acting is constant.
(D) dependent of origin.
Option b – independent of origin if the total external force acting is zero.
When a body rolls without slipping,
(A) there is no work done against friction.
(B) there is positive work done against friction.
(C) there is negative work done against friction.
(D) work done depends on the sense of rolling.
Option a – there is no work done against friction.
A wheel of the moment of inertia 1 kg m² is rotating about at a speed of 90 rad/s. It comes to rest in 2 minutes due to friction. The angular momentum of the wheel a minute before it stops rotating is
(A) 90 kg m²/s
(B) 64 kg m²/s
(C) 51 kg m²/s
(D) 45 kg m²/s
Option d – 45 kg m²/s
Which of the following is not the rotational analog of force? ( Rotational dynamics mcqs )
(A) Moment of force
(B) Impulse
(C) Torque
(D) Couple
Option b – Impulse
The ratio of the accelerations for a ring (mass m and radius R) rolling down an incline of angle ‘0’ without slipping and slipping down the incline without rolling is
(A) 1 : 2
(B) 2 : 3
(C) 2 : 5
(D) 2 : 1
Option a – 1 : 2
What should be the radius of a uniform cylinder of length 30 cm such that its moment of inertia about its perpendicular bisector should be minimum?
(A) 17.5 cm
(B) 24.5 cm
(C) 29.8 cm
(D) 31.2 cm
Option b – 24.5 cm
A rigid spherical body is spinning around an axis without any external torque. Due to changes in temperature, its volume increases by 2%. Its angular speed
(A) will increase approximately by 2%
(B) will decrease approximately by 2%
(C) will decrease approximately by 0.67 %
(D) will decrease approximately by 1.33%
Option d – will decrease approximately by 1.33%
If three particles A, B, and C are placed on the vertices of a triangle then the center of mass of a system
(A) will always be its geometric center.
(B) will never be its geometric center.
(C) will be its geometric center only if the triangle is equilateral.
(D) will be its geometric center if the triangle is equilateral and the particles are identical.
Option d – will be its geometric center if the triangle is equilateral and the particles are identical.
Choose an INCORRECT statement. For a spinning top,
(A) particles of the top lying on the axis of rotation of the top are stationary with respect to the spinning body of the top.
(B) point of contact of the top with the ground is fixed.
(C) its axis of rotation varies from time to time depending upon the cones it is sweeping in the space.
(D) its axis of rotation always passes through the point of contact with the ground.
Option c – its axis of rotation varies from time to time depending upon the cones it is sweeping in the space.
Assertion: For a very long pillar standing vertically, its center of gravity does not coincide with the center of mass. Reason: Centre of mass depends on the distribution of mass of the pillar.
(A) The assertion is True, Reason is True; Reason is a correct explanation for Assertion.
(B) The assertion is True, and Reason is True; Reason is not a correct explanation for Assertion.
(C) The assertion is True, Reason is False.
(D) The assertion is False, Reason is True.
Option b – The assertion is True, and Reason is True; Reason is not a correct explanation for Assertion.
A uniform wooden plank 4 m long and weighing 40 kg is resting on two supports 0.5 m from each end. A boy weighing 45 kg stands 1.5 m from one end of the wooden plank. What are the reactions to the support?
(A) 55 kg wt, 30 kg wt
(B) 45 kg wt, 40 kg wt
(C) 50 kg wt, 35 kg wt
(D) 63.7 kg wt, 21.3 kg wt
Option c – 50 kg wt, 35 kg wt
The moment of inertia of a ring about tangent in the plane of the ring as the axis of rotation
(A) 3 × M.I. of the ring along diameter as the axis of rotation.
(B) 1.5 M.I. of the ring along diameter as the axis of rotation.
(C) 3 × M.I. of ring about a line passing through its center and perpendicular to its plane as axis of rotation.
(D) 2 × M.I. of the ring along any tangent perpendicular to the plane of the ring as the axis of rotation.
Option a – 3 × M.I. of the ring along diameter as the axis of rotation.
A large value of the radius of gyration indicates ( Rotational dynamics mcqs )
(A) a large value of M.I. with mass distributed widely about an axis.
(B) a large value of M.I. with mass distributed widely away from the axis.
(C) a large value of M.I. with no information about mass distribution.
(D) a large value of M.I. and a large value of mass.
Option a – a large value of M.I. with mass distributed widely about an axis.
In pure translational motion at any instant of time, all particles of the body have the same velocity; the statement is true for
(A) an ice cube sliding across a floor.
(B) a steel beam sliding on an inclined plane.
(C) a pot getting shaped on a potter’s wheel.
(D) all of the above
Option b – a steel beam sliding on an inclined plane.
Which of the configuration’s positions of the center of mass coincides with their geometrical center?
(A) Uniform solid sphere
(B) Uniform rod
(C) Uniform circular ring
(D) all of the above
Option d – all of the above
The angular speed of the wheel is increased from 1200 rpm to 3600 rpm in 16 seconds such that it reaches 1600 rpm uniformly in 10 s and then uniformly reaches 3600 rpm, the ratio of angular accelerations observed respectively is
(A) 1:11
(B) 1:13
(C) 1:19
(D) 1:21
Option a – 1:11
For a body to possess only rotational motion, ( Rotational dynamics mcqs )
(A) the body should be balanced at its center of mass.
(B) the body should be balanced at its center of gravity.
(C) the body should be fixed along a line.
(D) the body should be rotated about an axis perpendicular to the plane of the body.
Option c – the body should be fixed along a line.
An engine of power 40 kW is installed on the rotor to attain a uniform angular speed of 200 rad/s. But the rotor is found to move with a uniform angular speed of 150 rad/s. What is the real power of machines?
(A) 50 kW
(B) 43 kW
(C) 30 kW
(D) 27 kW
Option c – 30 kW
Moment of inertia is a measure of (i) mass distribution of the body about the axis of rotation (ii) inertia of rotational motion of the body
(A) (i) only
(B) (ii) only
(C) (i) and (ii)
(D) (i) and (ii) for a uniform body
Option b – (ii) only
Assertion: Spokes are provided in a bicycle wheel. Reason: Mass of the bicycle wheel is less.
(A) The assertion is True, Reason is True; Reason is a correct explanation for Assertion.
(B) The assertion is True, and Reason is True; Reason is not a correct explanation for Assertion.
(C) The assertion is True, Reason is False.
(D) The assertion is False, Reason is True.
Option b – The assertion is True, and Reason is True; Reason is not a correct explanation for Assertion.
The radius of a solid sphere is 10 cm. The radius of gyration, when the axis of rotation is along a tangent, is
(A) 10 cm
(B) 11.8 cm
(C) 15 cm
(D) 14.3 cm
Option b – 11.8 cm
A flywheel attains an angular velocity of 32 rad/s from 4 rad/s in 7 s with constant angular acceleration. The total angle through which the flywheel has turned is
(A) 126 rad
(B) 98 rad
(C) 72 rad
(D) 24 rad
Option a – 126 rad
A massless cord is wound on the circular rim of the flywheel of mass 10 kg and radius 20 cm. When a cord is pulled steadily with 20 N unwinding 150 cm of cord, what is the K.E. of the wheel at this point? (Assume zero frictional loss)
(A) 17.8 J
(B) 20 J
(C) 23.8 J
(D) 30 J
Option d – 30 J
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