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:
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:
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:
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?
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:
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:
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:
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:
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:
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:
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?
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):
Answer: A. 40π
Explanation: ω = 2πf = 2π × (1200/60) = 2π × 20 = 40π rad/s.
Q13
Torque is the rotational analogue of:
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?
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):
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:
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:
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:
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?
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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):
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:
Answer: A. τθ
Explanation: Work done = τθ, analogous to F·s.
Q34
Angular velocity of second's hand of a clock is (rad/s):
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:
Answer: A. 40 J
Explanation: KE = ½ × 5 × 16 = 40 J.
Q36
The moment of inertia of a solid sphere about a tangent is:
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 = ?
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:
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:
Answer: A. 2 rad/s²
Explanation: α = (0-10)/5 = -2 rad/s².
Q40
A hoop rolls without slipping. Its total KE is:
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:
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?
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:
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):
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):
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:
Answer: A. 2.5 rad/s²
Explanation: α = (10-5)/2 = 2.5 rad/s².
Q47
The dimensional formula of moment of inertia is:
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?
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:
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:
Answer: A. 2π/T
Explanation: ω = 2π/T, where T is the time period.
📚 Complete Set of 50 Rotational Motion Questions
All questions with answers and explanations for NEET preparation
✅ Perfect for NEET Preparation | +4/-1 Marking Pattern | Previous Year & Expected Questions
📊 Track your progress: Each correct answer = +4 marks | Each wrong answer = -1 mark
We use cookies to improve your experience on our site. By using our site, you consent to cookies.
Manage your cookie preferences below:
Essential cookies enable basic functions and are necessary for the proper function of the website.
These cookies are needed for adding comments on this website.
Google Tag Manager simplifies the management of marketing tags on your website without code changes.
Statistics cookies collect information anonymously. This information helps us understand how visitors use our website.
Google Analytics is a powerful tool that tracks and analyzes website traffic for informed marketing decisions.
Service URL: policies.google.com (opens in a new window)
Marketing cookies are used to track visitors to websites. The intention is to show ads that are relevant and engaging to the individual user.
Pinterest Tag is a web analytics service that tracks and reports website traffic.
Service URL: policy.pinterest.com (opens in a new window)
You can find more information in our Cookie Policy.
Abonnez-vous pour poursuivre la lecture et avoir accès à l’ensemble des archives.
Abonnez-vous pour poursuivre la lecture et avoir accès à l’ensemble des archives.