Q.1 The moment of inertia of a uniform thin rod of length L and mass M about an axis perpendicular to the rod and passing through its center is:
ML²/12
ML²/3
ML²/4
ML²/2
Explanation - For a uniform thin rod about its center, moment of inertia I = (1/12)ML² according to the standard formula.
Correct answer is: ML²/12
Q.2 The rotational analogue of force in linear motion is:
Work
Torque
Angular momentum
Power
Explanation - Torque plays the same role in rotational motion as force does in linear motion.
Correct answer is: Torque
Q.3 A disc is rotating with constant angular velocity. Which quantity remains constant?
Linear velocity of points
Tangential acceleration
Angular velocity
Angular acceleration
Explanation - In uniform rotational motion, angular velocity remains constant while tangential velocity varies with radius.
Correct answer is: Angular velocity
Q.4 If a wheel makes 120 revolutions per minute, its angular velocity in rad/s is approximately:
4π
6π
8π
10π
Explanation - Angular velocity ω = 2π × (revolutions per second). 120 rpm = 2 rev/s, so ω = 2π × 2 = 4π rad/s.
Correct answer is: 4π
Q.5 The unit of moment of inertia is:
kg·m/s
kg·m²
kg·m²/s
N·m
Explanation - Moment of inertia depends on mass and square of distance, so its SI unit is kg·m².
Correct answer is: kg·m²
Q.6 The parallel axis theorem relates the moment of inertia about any axis to that about a parallel axis through:
Center of gravity
End point
Midpoint
Any point on the body
Explanation - The theorem states I = I_cm + Md², where I_cm is about the center of mass axis.
Correct answer is: Center of gravity
Q.7 A rigid body is rotating with angular velocity ω. Its rotational kinetic energy is given by:
(1/2)Iω
(1/2)Iω²
Iω²
Iω
Explanation - The rotational kinetic energy formula is analogous to linear kinetic energy: KE = (1/2)mv² → (1/2)Iω².
Correct answer is: (1/2)Iω²
Q.8 The SI unit of angular velocity is:
rad/s
rad
s
m/s
Explanation - Angular velocity is measured as radians per second.
Correct answer is: rad/s
Q.9 The torque acting on a body is zero. Which of the following must be constant?
Angular velocity
Moment of inertia
Angular momentum
Kinetic energy
Explanation - When net external torque is zero, angular momentum remains conserved according to the law of conservation of angular momentum.
Correct answer is: Angular momentum
Q.10 A particle moving in a circle of radius r with constant speed v has angular acceleration:
v²/r
0
v/r
r/v
Explanation - If the angular velocity is constant, angular acceleration is zero even though the linear acceleration may not be.
Correct answer is: 0
Q.11 The physical quantity that resists change in rotational motion is:
Mass
Torque
Angular acceleration
Moment of inertia
Explanation - Moment of inertia plays the same role in rotational motion as mass does in linear motion.
Correct answer is: Moment of inertia
Q.12 If a uniform solid sphere rolls without slipping, the ratio of its translational kinetic energy to total kinetic energy is:
2/5
3/5
5/7
7/10
Explanation - Total KE = Translational + Rotational = (1/2)mv² + (1/2)Iω². For a sphere, I = (2/5)mr² and ω = v/r, giving Translational/Total = 5/7.
Correct answer is: 5/7
Q.13 The angular momentum of a particle is perpendicular to:
Linear momentum
Velocity
Torque
Plane of motion
Explanation - Angular momentum is given by L = r × p, which is perpendicular to the plane containing r and p.
Correct answer is: Plane of motion
Q.14 Two bodies of masses 2 kg and 3 kg are rotating with equal angular velocity. The ratio of their moments of inertia is 2:3. The ratio of their rotational kinetic energies is:
2:3
3:2
4:9
9:4
Explanation - Rotational KE = (1/2)Iω². Since ω is the same, KE ratio = I ratio = 2:3.
Correct answer is: 2:3
Q.15 The dimension of torque is equivalent to that of:
Work
Force
Moment of inertia
Linear momentum
Explanation - Torque = Force × Distance → dimensions are the same as Work (ML²T⁻²).
Correct answer is: Work
Q.16 A body rolling without slipping has:
Only rotational motion
Only translational motion
Both rotational and translational motion
No motion
Explanation - Rolling without slipping combines rotation and translation such that point of contact is momentarily at rest.
Correct answer is: Both rotational and translational motion
Q.17 A flywheel increases the stability of a machine by:
Storing potential energy
Increasing torque
Storing rotational kinetic energy
Decreasing angular velocity
Explanation - Flywheels store rotational kinetic energy to reduce fluctuations in machine speed.
Correct answer is: Storing rotational kinetic energy
Q.18 A disc and a ring of same mass and radius are released from the top of an incline. Which will reach the bottom first?
Disc
Ring
Both together
Cannot be determined
Explanation - Disc has lower moment of inertia relative to its mass, so it accelerates faster and reaches first.
Correct answer is: Disc
Q.19 In rotational motion, the term analogous to linear momentum (mv) is:
Moment of inertia
Torque
Angular velocity
Angular momentum
Explanation - Linear momentum in rotation is replaced by Angular momentum L = Iω.
Correct answer is: Angular momentum
Q.20 The work done by a torque in rotating a body through an angle θ is:
τθ
τ/θ
θ/τ
2τθ
Explanation - Work = Torque × Angular displacement (θ).
Correct answer is: τθ
Q.21 For a given angular momentum, the kinetic energy of a rotating body is minimum when the axis of rotation passes through:
Center of gravity
Edge
Any point
Surface
Explanation - The moment of inertia is minimum when axis passes through center of mass, giving minimum KE for given angular momentum.
Correct answer is: Center of gravity
Q.22 The condition for pure rolling is:
v = ωr
v > ωr
v < ωr
v = 0
Explanation - For rolling without slipping, the linear velocity of the center equals tangential velocity at point of contact.
Correct answer is: v = ωr
Q.23 If angular velocity doubles, the rotational kinetic energy becomes:
Half
Same
Double
Four times
Explanation - KE ∝ ω². Doubling ω makes KE four times greater.
Correct answer is: Four times
Q.24 The moment of inertia of a hollow cylinder about its own axis is:
MR²/2
MR²
2MR²
MR²/4
Explanation - For a hollow cylinder, all mass is at distance R from axis, so I = MR².
Correct answer is: MR²
Q.25 A spinning skater pulls in her arms. Her rotational speed:
Decreases
Increases
Remains same
Stops
Explanation - Pulling arms inward decreases moment of inertia, and by conservation of angular momentum, angular velocity increases.
Correct answer is: Increases
Q.26 A body rotates about a fixed axis with an angular acceleration of 4 rad/s². If its initial angular velocity is 2 rad/s, what will be its angular velocity after 3 seconds?
10 rad/s
8 rad/s
14 rad/s
6 rad/s
Explanation - Using formula: ω = ω₀ + αt = 2 + (4 × 3) = 14 rad/s.
Correct answer is: 14 rad/s
Q.27 Moment of inertia depends on which factor the most?
Shape of the body
Mass distribution
Material of the body
Elasticity
Explanation - Moment of inertia is directly related to how mass is distributed about the axis of rotation.
Correct answer is: Mass distribution
Q.28 The SI unit of torque is:
Joule
Newton
Newton-meter
Pascal
Explanation - Torque = Force × Perpendicular distance. SI unit = Newton-meter.
Correct answer is: Newton-meter
Q.29 If a solid sphere and a hollow sphere of the same mass and radius roll down an inclined plane, which reaches the bottom first?
Solid sphere
Hollow sphere
Both at the same time
Depends on slope
Explanation - Solid sphere has a lower moment of inertia, so it accelerates faster.
Correct answer is: Solid sphere
Q.30 Which physical quantity is analogous to linear momentum in rotational motion?
Angular displacement
Torque
Angular momentum
Moment of inertia
Explanation - Angular momentum is analogous to linear momentum in rotational dynamics.
Correct answer is: Angular momentum
Q.31 A wheel rotating at 10 rad/s comes to rest in 20 seconds. What is its angular deceleration?
-0.25 rad/s²
-0.5 rad/s²
-0.75 rad/s²
-1.0 rad/s²
Explanation - Using α = (ω - ω₀) / t = (0 - 10)/20 = -0.5 rad/s².
Correct answer is: -0.5 rad/s²
Q.32 The rotational kinetic energy of a rotating rigid body is given by:
1/2 mv²
1/2 Iω²
Iω
mgh
Explanation - The formula for rotational kinetic energy is ½ × Moment of Inertia × Angular Velocity².
Correct answer is: 1/2 Iω²
Q.33 Which has a greater moment of inertia for the same mass and radius?
Solid sphere
Hollow sphere
Solid cylinder
Thin ring
Explanation - Moment of inertia increases as more mass is distributed farther from the axis.
Correct answer is: Thin ring
Q.34 Torque is the rotational analogue of which quantity?
Force
Work
Energy
Power
Explanation - Torque causes angular acceleration just like force causes linear acceleration.
Correct answer is: Force
Q.35 The unit of angular velocity is:
m/s
rad/s
rad
m/s²
Explanation - Angular velocity measures change in angular displacement per unit time in radians per second.
Correct answer is: rad/s
Q.36 A flywheel with moment of inertia 0.5 kg·m² rotates with 4 rad/s. Its kinetic energy is:
2 J
4 J
6 J
8 J
Explanation - KE = ½ Iω² = 0.5 × 0.5 × (4)² = 4 J.
Correct answer is: 4 J
Q.37 If angular velocity is constant, angular acceleration is:
Zero
Positive
Negative
Undefined
Explanation - Angular acceleration is the rate of change of angular velocity. If angular velocity is constant, it's zero.
Correct answer is: Zero
Q.38 For a uniform solid disk of radius R and mass M, moment of inertia about its central axis is:
MR²
½ MR²
⅓ MR²
¼ MR²
Explanation - Standard formula: I = ½ MR² for a solid disk about its central axis.
Correct answer is: ½ MR²
Q.39 Which law governs rotational motion analogous to Newton's second law?
τ = Iα
L = Iω
F = ma
P = IV
Explanation - Torque equals moment of inertia multiplied by angular acceleration, analogous to F = ma.
Correct answer is: τ = Iα
Q.40 In rolling motion, the point of contact with the ground is:
Stationary
Moving forward
Moving backward
Accelerating
Explanation - At the point of contact, relative velocity is zero.
Correct answer is: Stationary
Q.41 A body of mass 2 kg has a moment of inertia of 0.8 kg·m². Its angular acceleration when a torque of 4 N·m is applied is:
5 rad/s²
4 rad/s²
3 rad/s²
2 rad/s²
Explanation - α = τ / I = 4 / 0.8 = 5 rad/s².
Correct answer is: 5 rad/s²
Q.42 Angular momentum is conserved when:
External torque is zero
Angular acceleration is zero
Angular velocity is constant
Moment of inertia is constant
Explanation - Just as linear momentum is conserved when no external force acts, angular momentum is conserved when no external torque acts.
Correct answer is: External torque is zero
Q.43 The rotational equivalent of work done is:
Torque × Angular displacement
Moment of inertia × Angular velocity
Torque × Time
Power × Time
Explanation - Work in rotational motion = τ × θ (in radians).
Correct answer is: Torque × Angular displacement
Q.44 For a hoop of radius R and mass M, the moment of inertia about its diameter is:
MR²
½ MR²
¼ MR²
⅔ MR²
Explanation - Using the perpendicular axis theorem: I_diameter = ½ MR².
Correct answer is: ½ MR²
Q.45 The vector quantity among the following is:
Moment of inertia
Angular velocity
Rotational kinetic energy
Angular displacement
Explanation - Angular velocity has magnitude and direction, making it a vector quantity.
Correct answer is: Angular velocity
Q.46 The moment of inertia of a thin rod of mass M and length L about its center is:
ML²/3
ML²/4
ML²/12
ML²/2
Explanation - Standard formula for a uniform rod about its center: I = (1/12) ML².
Correct answer is: ML²/12
Q.47 Which theorem relates the moment of inertia about any axis to the moment of inertia about a parallel axis?
Steiner's theorem
Newton's theorem
Bernoulli's theorem
Lami's theorem
Explanation - Steiner's theorem (parallel axis theorem) relates I_parallel = I_cm + Md².
Correct answer is: Steiner's theorem
Q.48 Which quantity determines the rotational analogue of mass?
Torque
Moment of inertia
Angular velocity
Angular displacement
Explanation - Moment of inertia plays the same role in rotational motion as mass does in linear motion.
Correct answer is: Moment of inertia
Q.49 The relation between linear velocity (v) and angular velocity (ω) for rolling motion is:
v = ω/R
v = ωR
v = ω²R
v = ω + R
Explanation - For rolling without slipping, v = ωR.
Correct answer is: v = ωR
Q.50 The direction of angular momentum vector is given by:
Left-hand rule
Right-hand rule
Both hands rule
None of these
Explanation - Curl the fingers of your right hand in the direction of rotation; the thumb shows the direction of angular momentum.
Correct answer is: Right-hand rule