🔄 NEET Physics: Rotational Motion Practice Q&A

50 MCQs with Answers & Explanations | +4/-1 Pattern

Q1

Moment of inertia of a thin circular ring of mass M and radius R about an axis through its centre and perpendicular to its plane is:

A. MR²
B. ½MR²
C. ⅔MR²
D. ⅕MR²
✅ Show Answer & Explanation

Answer: A. MR²
Explanation: For a ring, all mass is at distance R from the axis, so I = MR².

Q2

A torque of 20 Nm produces an angular acceleration of 4 rad/s². The moment of inertia is:

A. 5 kg m²
B. 80 kg m²
C. 0.2 kg m²
D. 24 kg m²
✅ Show Answer & Explanation

Answer: A. 5 kg m²
Explanation: τ = Iα → I = τ/α = 20/4 = 5 kg m².

Q3

Angular momentum of a rigid body is given by:

A. Iω
B. mv
C. mω²
D. Iα
✅ Show Answer & Explanation

Answer: A. Iω
Explanation: Angular momentum L = Iω, where I is moment of inertia and ω is angular velocity.

Q4

A disc and a ring have same mass and radius. Which has greater moment of inertia about its central axis?

A. Ring
B. Disc
C. Both equal
D. Depends on material
✅ Show Answer & Explanation

Answer: A. Ring
Explanation: Ring: MR², Disc: ½MR², so ring has larger moment of inertia.

Q5

The radius of gyration of a body about an axis is defined as:

A. √(I/M)
B. I/M
C. M/I
D. √(M/I)
✅ Show Answer & Explanation

Answer: A. √(I/M)
Explanation: Radius of gyration K = √(I/M), where I = MK².

Q6

A solid sphere of mass M and radius R rotates about its diameter. Its moment of inertia is:

A. ⅖MR²
B. ⅔MR²
C. ½MR²
D. MR²
✅ Show Answer & Explanation

Answer: A. ⅖MR²
Explanation: For solid sphere about diameter: I = (2/5)MR².

Q7

A particle of mass 2 kg moves in a circle of radius 0.5 m with angular speed 10 rad/s. Its angular momentum is:

A. 5 kg m²/s
B. 10 kg m²/s
C. 20 kg m²/s
D. 1 kg m²/s
✅ Show Answer & Explanation

Answer: A. 5 kg m²/s
Explanation: L = mr²ω = 2 × (0.5)² × 10 = 2 × 0.25 × 10 = 5 kg m²/s.

Q8

A wheel of I = 2 kg m² rotates at 5 rad/s. Torque required to stop it in 10 s is:

A. 1 Nm
B. 2 Nm
C. 0.5 Nm
D. 10 Nm
✅ Show Answer & Explanation

Answer: A. 1 Nm
Explanation: α = (0-5)/10 = -0.5 rad/s², τ = Iα = 2 × 0.5 = 1 Nm.

Q9

Moment of inertia of a thin rod of length L, mass M about an axis perpendicular to rod through its centre is:

A. ML²/12
B. ML²/3
C. ML²/6
D. ML²/2
✅ Show Answer & Explanation

Answer: A. ML²/12
Explanation: For a thin rod about its centre, I = ML²/12.

Q10

If the angular velocity doubles, the rotational kinetic energy becomes:

A. 4 times
B. 2 times
C. 8 times
D. same
✅ Show Answer & Explanation

Answer: A. 4 times
Explanation: KE = ½Iω², so ω doubles → KE becomes 4 times.

Q11

A solid cylinder and a hollow cylinder have same mass and radius. Which rolls down an incline faster?

A. Solid cylinder
B. Hollow cylinder
C. Both same
D. Depends on angle
✅ Show Answer & Explanation

Answer: A. Solid cylinder
Explanation: Solid cylinder has smaller moment of inertia (½MR² vs MR²), so it accelerates faster.

Q12

A body rotating at 1200 rpm has angular velocity (rad/s):

A. 40π
B. 20π
C. 10π
D. 80π
✅ Show Answer & Explanation

Answer: A. 40π
Explanation: ω = 2πf = 2π × (1200/60) = 2π × 20 = 40π rad/s.

Q13

Torque is the rotational analogue of:

A. Force
B. Momentum
C. Work
D. Energy
✅ Show Answer & Explanation

Answer: A. Force
Explanation: τ = Iα is analogous to F = ma, so torque is the rotational analogue of force.

Q14

A dancer pulls her arms closer during a spin. What happens to her angular velocity?

A. Increases
B. Decreases
C. Remains same
D. Becomes zero
✅ Show Answer & Explanation

Answer: A. Increases
Explanation: Conservation of angular momentum L = Iω. When she pulls her arms in, I decreases, so ω increases.

Q15

Moment of inertia of a rectangular plate about an axis perpendicular to plate through centre (mass M, sides a,b):

A. M(a²+b²)/12
B. M(a²+b²)/6
C. M(a²+b²)/3
D. M(a²+b²)/24
✅ Show Answer & Explanation

Answer: A. M(a²+b²)/12
Explanation: For a rectangular plate about perpendicular axis through centre, I = M(a²+b²)/12.

Q16

Angular acceleration is defined as:

A. dω/dt
B. dθ/dt
C. dL/dt
D. τ/I
✅ Show Answer & Explanation

Answer: A. dω/dt
Explanation: Angular acceleration α = dω/dt, the rate of change of angular velocity.

Q17

A force of 10 N acts tangentially on a wheel of radius 0.2 m. Torque produced is:

A. 2 Nm
B. 0.5 Nm
C. 50 Nm
D. 0.02 Nm
✅ Show Answer & Explanation

Answer: A. 2 Nm
Explanation: τ = rF = 0.2 × 10 = 2 Nm.

Q18

A thin circular disc of mass M and radius R has moment of inertia about its diameter:

A. MR²/4
B. MR²/2
C. MR²/8
D. MR²/6
✅ Show Answer & Explanation

Answer: A. MR²/4
Explanation: Using perpendicular axis theorem, I_diameter = MR²/4.

Q19

A ring and a disc roll down an incline. Which reaches bottom first?

A. Disc
B. Ring
C. Both together
D. Depends on mass
✅ Show Answer & Explanation

Answer: A. Disc
Explanation: Disc has smaller k²/R² ratio (0.5 vs 1), so greater acceleration.

Q20

The angular momentum of a system is conserved if:

A. Net external torque is zero
B. Net external force is zero
C. Angular velocity constant
D. Moment of inertia constant
✅ Show Answer & Explanation

Answer: A. Net external torque is zero
Explanation: τ_ext = dL/dt = 0 means L is constant.

Q21

A wheel starts from rest and gains angular velocity 20 rad/s in 4 s. Angular acceleration is:

A. 5 rad/s²
B. 4 rad/s²
C. 80 rad/s²
D. 0.2 rad/s²
✅ Show Answer & Explanation

Answer: A. 5 rad/s²
Explanation: α = (20-0)/4 = 5 rad/s².

Q22

A body of moment of inertia 3 kg m² rotates with 10 rad/s. Its angular momentum is:

A. 30 kg m²/s
B. 3.33 kg m²/s
C. 0.3 kg m²/s
D. 300 kg m²/s
✅ Show Answer & Explanation

Answer: A. 30 kg m²/s
Explanation: L = Iω = 3 × 10 = 30 kg m²/s.

Q23

Rotational kinetic energy of a body is 200 J and angular velocity 10 rad/s. Moment of inertia is:

A. 4 kg m²
B. 2 kg m²
C. 20 kg m²
D. 0.5 kg m²
✅ Show Answer & Explanation

Answer: A. 4 kg m²
Explanation: KE = ½Iω² → 200 = ½ × I × 100 → I = 4 kg m².

Q24

A solid sphere rolls without slipping. Ratio of translational KE to rotational KE is:

A. 5/2
B. 2/5
C. 7/5
D. 5/7
✅ Show Answer & Explanation

Answer: A. 5/2
Explanation: KE_trans = ½mv², KE_rot = ⅕mv², ratio = (½)/(⅕) = 5/2.

Q25

Moment of inertia of a thin spherical shell about its diameter:

A. ⅔MR²
B. ⅖MR²
C. MR²
D. ½MR²
✅ Show Answer & Explanation

Answer: A. ⅔MR²
Explanation: For thin spherical shell, I = (2/3)MR².

Q26

A torque of 100 Nm acts on a flywheel of I=20 kg m² for 5 s. Angular impulse is:

A. 500 Nms
B. 20 Nms
C. 100 Nms
D. 2000 Nms
✅ Show Answer & Explanation

Answer: A. 500 Nms
Explanation: Angular impulse = τ × t = 100 × 5 = 500 Nms.

Q27

A particle moves in a circle with constant angular speed. Its angular acceleration is:

A. Zero
B. Constant non-zero
C. Variable
D. Infinite
✅ Show Answer & Explanation

Answer: A. Zero
Explanation: Constant ω means α = dω/dt = 0.

Q28

Two rings have same mass but radii R and 2R. Ratio of moments of inertia about axis through centre:

A. 1:4
B. 1:2
C. 2:1
D. 4:1
✅ Show Answer & Explanation

Answer: A. 1:4
Explanation: I ∝ R², so I₁/I₂ = (R²)/(4R²) = 1:4.

Q29

A disc of mass 2 kg and radius 0.5 m. Moment of inertia about perpendicular axis through centre:

A. 0.25 kg m²
B. 0.5 kg m²
C. 0.125 kg m²
D. 1 kg m²
✅ Show Answer & Explanation

Answer: A. 0.25 kg m²
Explanation: I = ½MR² = 0.5 × 2 × 0.25 = 0.25 kg m².

Q30

The radius of gyration of a disc about its diameter is:

A. R/2
B. R/√2
C. R/√3
D. R/4
✅ Show Answer & Explanation

Answer: A. R/2
Explanation: I_diameter = MR²/4 = MK² → K = R/2.

Q31

A hollow cylinder has same mass and radius as solid cylinder. Their moments of inertia ratio I_hollow/I_solid:

A. 2:1
B. 1:2
C. 1:1
D. 4:1
✅ Show Answer & Explanation

Answer: A. 2:1
Explanation: I_hollow = MR², I_solid = ½MR² → ratio = 2:1.

Q32

A rod of length 1 m, mass 3 kg rotates about one end. Moment of inertia is (ML²/3):

A. 1 kg m²
B. 3 kg m²
C. 0.33 kg m²
D. 9 kg m²
✅ Show Answer & Explanation

Answer: A. 1 kg m²
Explanation: I = ML²/3 = 3 × 1/3 = 1 kg m².

Q33

Work done by torque τ when angular displacement is θ:

A. τθ
B. τ/θ
C. τ×t
D. Iω²/2
✅ Show Answer & Explanation

Answer: A. τθ
Explanation: Work done = τθ, analogous to F·s.

Q34

Angular velocity of second's hand of a clock is (rad/s):

A. π/30
B. π/60
C. 2π/60
D. π/180
✅ Show Answer & Explanation

Answer: A. π/30
Explanation: ω = 2π/T, T=60 s → ω = 2π/60 = π/30 rad/s.

Q35

A rotating body has I = 5 kg m², ω = 4 rad/s. Its rotational KE is:

A. 40 J
B. 80 J
C. 20 J
D. 10 J
✅ Show Answer & Explanation

Answer: A. 40 J
Explanation: KE = ½ × 5 × 16 = 40 J.

Q36

The moment of inertia of a solid sphere about a tangent is:

A. 7/5 MR²
B. 2/5 MR²
C. 3/5 MR²
D. MR²
✅ Show Answer & Explanation

Answer: A. 7/5 MR²
Explanation: By parallel axis: I_tangent = I_cm + MR² = (2/5)MR² + MR² = (7/5)MR².

Q37

A torque of 8 Nm produces angular acceleration 2 rad/s². I = ?

A. 4 kg m²
B. 16 kg m²
C. 0.25 kg m²
D. 10 kg m²
✅ Show Answer & Explanation

Answer: A. 4 kg m²
Explanation: I = τ/α = 8/2 = 4 kg m².

Q38

A particle of mass m moves in circle radius r with speed v. Angular momentum about centre:

A. mvr
B. mv/r
C. mrv²
D. mr²v
✅ Show Answer & Explanation

Answer: A. mvr
Explanation: L = mvr, since L = r × p.

Q39

A disc rotating at 10 rad/s is brought to rest in 5 s by constant torque. Angular deceleration:

A. 2 rad/s²
B. 0.5 rad/s²
C. 50 rad/s²
D. 5 rad/s²
✅ Show Answer & Explanation

Answer: A. 2 rad/s²
Explanation: α = (0-10)/5 = -2 rad/s².

Q40

A hoop rolls without slipping. Its total KE is:

A. mv²
B. ½mv²
C. ¾mv²
D. ⅔mv²
✅ Show Answer & Explanation

Answer: A. mv²
Explanation: KE_total = ½mv² + ½Iω² = ½mv² + ½(mR²)(v²/R²) = mv².

Q41

A body is in pure rotation. The point where instantaneous velocity is zero:

A. Axis of rotation
B. Centre of mass
C. Periphery
D. No point
✅ Show Answer & Explanation

Answer: A. Axis of rotation
Explanation: Points on the axis of rotation have zero velocity in pure rotation.

Q42

If net torque on a body is zero, which quantity is conserved?

A. Angular momentum
B. Angular velocity
C. Moment of inertia
D. Rotational KE
✅ Show Answer & Explanation

Answer: A. Angular momentum
Explanation: τ = dL/dt = 0 → L is constant.

Q43

A wheel of radius 0.3 m rolls without slipping. If its angular speed is 20 rad/s, linear speed of centre is:

A. 6 m/s
B. 0.6 m/s
C. 60 m/s
D. 20 m/s
✅ Show Answer & Explanation

Answer: A. 6 m/s
Explanation: v = Rω = 0.3 × 20 = 6 m/s.

Q44

Moment of inertia of a solid cylinder about its axis (length L, radius R):

A. ½MR²
B. M(R²/4 + L²/12)
C. MR²/2 + ML²/12
D. MR²
✅ Show Answer & Explanation

Answer: A. ½MR²
Explanation: About cylindrical axis, I = ½MR², independent of length.

Q45

A rod of length L is bent into a ring. Its moment of inertia about axis perpendicular through centre (mass M):

A. ML²/(4π²)
B. ML²/(2π²)
C. ML²/(π²)
D. ML²/2
✅ Show Answer & Explanation

Answer: A. ML²/(4π²)
Explanation: Radius R = L/(2π), I = MR² = M(L²/(4π²)).

Q46

A flywheel increases speed from 5 to 10 rad/s in 2 s. Angular acceleration:

A. 2.5 rad/s²
B. 5 rad/s²
C. 2 rad/s²
D. 7.5 rad/s²
✅ Show Answer & Explanation

Answer: A. 2.5 rad/s²
Explanation: α = (10-5)/2 = 2.5 rad/s².

Q47

The dimensional formula of moment of inertia is:

A. ML²
B. ML²T⁻²
C. MLT⁻²
D. ML²T⁻¹
✅ Show Answer & Explanation

Answer: A. ML²
Explanation: I = mr² gives dimensions [M][L²] = ML².

Q48

A solid disc and solid sphere have same mass and radius. Which has larger I about central axis?

A. Disc
B. Sphere
C. Equal
D. Cannot say
✅ Show Answer & Explanation

Answer: A. Disc
Explanation: I_disc = ½MR², I_sphere = ⅖MR² = 0.4MR², so disc is larger.

Q49

A body rolling down an incline with slipping has:

A. No rolling
B. Pure rolling
C. Mixed motion
D. Stationary
✅ Show Answer & Explanation

Answer: A. No rolling
Explanation: With slipping, it is not pure rolling; friction is insufficient.

Q50

Angular frequency of a particle in uniform circular motion is related to time period as:

A. 2π/T
B. T/2π
C. 2πT
D. 1/T
✅ Show Answer & Explanation

Answer: A. 2π/T
Explanation: ω = 2π/T, where T is the time period.

📝 Key Rotational Motion Formulae

τ = Iα L = Iω KE = ½Iω² I = Σmr² ω = ω₀ + αt θ = ω₀t + ½αt² ω² = ω₀² + 2αθ

📚 Complete Set of 50 Rotational Motion Questions
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