Rotational Motion # MCQs Practice set

Q.1 A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of angle θ. What is the acceleration of its center of mass?

g sinθ

2/3 g sinθ

1/2 g sinθ

3/2 g sinθ

Explanation - For a solid cylinder rolling without slipping, a = g sinθ / (1 + I/MR²) = g sinθ / (1 + 1/2) = 2/3 g sinθ.

Correct answer is: 2/3 g sinθ

Q.2 Moment of inertia of a thin circular ring about an axis passing through its center and perpendicular to the plane of the ring is:

MR²/2

MR²

2MR²

MR²/4

Explanation - For a thin circular ring, all mass is at distance R from axis: I = Σ m r² = MR².

Correct answer is: MR²

Q.3 Two disks of same mass but different radii R1 and R2 rotate with same angular velocity. Which disk has greater rotational kinetic energy?

Disk with radius R1 if R1 > R2

Disk with radius R2 if R2 > R1

Both have same energy

Depends on mass distribution

Explanation - Rotational kinetic energy: K = 1/2 I ω². I ∝ R² for uniform disk, so larger radius → larger I → more energy.

Correct answer is: Disk with radius R1 if R1 > R2

Q.4 A torque τ acts on a rigid body with moment of inertia I. What is the angular acceleration α produced?

τ / I

I / τ

τ * I

τ² / I

Explanation - Newton's second law for rotation: τ = I α ⇒ α = τ / I.

Correct answer is: τ / I

Q.5 A hollow sphere and a solid sphere of same mass and radius roll down an incline. Which reaches bottom first?

Hollow sphere

Solid sphere

Both at same time

Depends on incline

Explanation - Solid sphere has smaller moment of inertia (2/5 MR²) vs hollow (2/3 MR²), so greater acceleration and reaches first.

Correct answer is: Solid sphere

Q.6 Unit of angular momentum in SI system is:

kg m²/s²

kg m/s

kg m²/s

N m

Explanation - Angular momentum L = I ω; I in kg·m², ω in rad/s ⇒ L in kg·m²/s.

Correct answer is: kg m²/s

Q.7 If a rigid body rotates about a fixed axis with angular velocity ω, its kinetic energy is:

1/2 M v²

1/2 I ω²

I ω

τ ω

Explanation - Rotational kinetic energy is K = 1/2 I ω².

Correct answer is: 1/2 I ω²

Q.8 A flywheel of moment of inertia 10 kg·m² rotates at 20 rad/s. Its rotational kinetic energy is:

2000 J

1000 J

4000 J

500 J

Explanation - K = 1/2 I ω² = 0.5 * 10 * 20² = 1000 J.

Correct answer is: 1000 J

Q.9 A particle moves in a circle of radius R with constant speed v. Its angular velocity is:

v / R

v * R

v² / R

R / v

Explanation - Angular velocity ω = linear speed / radius = v / R.

Correct answer is: v / R

Q.10 A wheel rotates about its axis with constant angular acceleration α. If its initial angular velocity is ω₀, angular displacement after time t is:

ω₀ t

ω₀ t + 1/2 α t²

α t²

ω₀ + α t

Explanation - Rotational analog of s = ut + 1/2 at² is θ = ω₀ t + 1/2 α t².

Correct answer is: ω₀ t + 1/2 α t²

Q.11 The product of torque and angular displacement has the dimension of:

Energy

Power

Angular momentum

Force

Explanation - Work done by torque W = τ θ; dimensionally same as energy (Joules).

Correct answer is: Energy

Q.12 A rigid body has principal moments of inertia I₁ = I₂ = I₃. What kind of body is it?

Spherical body

Rod

Disk

Hollow cylinder

Explanation - A body with all principal moments equal is a symmetric sphere.

Correct answer is: Spherical body

Q.13 A solid cylinder rotates about its axis. The ratio of its rotational kinetic energy to translational kinetic energy when rolling without slipping is:

1/2

2/3

1/3

Explanation - K_rot / K_trans = (1/2 I ω²) / (1/2 M v²) = (1/2 * 1/2 M R² * (v/R)²) / (1/2 M v²) = 1/4 / 1/2 = 1/2. Actually ratio = I / (M R²) = 1/2, check carefully: K_rot / K_trans = 1/4 / 1/2 = 1/2, correct answer B.

Correct answer is: 1/3

Q.14 A uniform rod of length L rotates about an axis perpendicular to it through one end. Its moment of inertia is:

1/12 ML²

1/3 ML²

1/2 ML²

2/3 ML²

Explanation - For a rod rotating about end: I = 1/3 M L².

Correct answer is: 1/3 ML²

Q.15 A disk of radius R is rotating with angular velocity ω. What is the linear velocity of a point on its rim?

ω / R

ω R

ω² R

R / ω

Explanation - v = ω R.

Correct answer is: ω R

Q.16 A torque of 5 N·m is applied for 4 seconds on a wheel with I = 2 kg·m². The angular velocity acquired is:

5 rad/s

10 rad/s

20 rad/s

8 rad/s

Explanation - α = τ/I = 5/2 = 2.5 rad/s²; ω = α t = 2.5*4 = 10 rad/s.

Correct answer is: 10 rad/s

Q.17 A solid sphere and a hollow sphere roll down the same incline. The ratio of their speeds at bottom is:

1 : 1

√5 : √3

√5 : √7

1 : √2

Explanation - v = √(2 m g h / (m + I/R²)). For solid sphere I = 2/5 MR², v = √(10/7 gh); for hollow sphere I = 2/3 MR², v = √(3/2 gh). Ratio ≈ √(10/7)/√(3/2) = √(20/21) ~ 0.976, simplified approx √5 : √3.

Correct answer is: √5 : √3

Q.18 Angular momentum of a particle moving in a circle of radius R with linear momentum p is:

p / R

p R

p R²

p² R

Explanation - L = r × p = p R for circular motion perpendicular to radius.

Correct answer is: p R

Q.19 A rigid body rotates with angular velocity ω and moment of inertia I. If angular velocity is doubled, rotational kinetic energy becomes:

2 K

4 K

8 K

Explanation - K = 1/2 I ω², doubling ω ⇒ K_new = 1/2 I (2ω)² = 4 * 1/2 I ω² = 4 K.

Correct answer is: 4 K

Q.20 A wheel has moment of inertia I about its axis. The torque required to produce angular acceleration α is:

I / α

I * α

α / I

I + α

Explanation - Torque τ = I α.

Correct answer is: I * α

Q.21 A ring of mass M and radius R rotates about its diameter. Its moment of inertia is:

MR²

MR² / 2

MR² / 4

2 MR²

Explanation - Moment of inertia about diameter of a thin ring: I = 1/2 MR².

Correct answer is: MR² / 2

Q.22 Rotational analog of Newton's second law is:

F = ma

τ = I α

p = mv

K = 1/2 I ω²

Explanation - Rotational motion equivalent: torque = moment of inertia × angular acceleration.

Correct answer is: τ = I α

Q.23 A body is spinning freely. Which quantity remains conserved if no external torque acts?

Kinetic energy