83 free MCQs on System of Particles and Rotational Motion, each with its own worked answer and explanation. Moment of inertia, torque, angular momentum, rolling motion. Very high JEE weightage.
Take the timed System of Particles and Rotational Motion chapterwise test →83 practice questions on System of Particles and Rotational Motion, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the System of Particles and Rotational Motion notes.
Torque about axis O equals the force F multiplied by the perpendicular distance r⊥ from the axis to the line of action of the force, producing rotation.
Q1.
The moment of inertia of a body depends on:
Q2.
The centre of mass of a uniform triangular plate lies at its:
Q3.
A couple acting on a rigid body produces:
Q4.
The radius of gyration of a body has the same dimensions as:
Q5.
What is the moment of inertia of a solid sphere of mass M and radius R about its diameter?
Q6.
The angular equivalent of Newton's second law (F = ma) is:
Q7.
A ring, a disk, and a solid sphere of equal mass and radius roll down an incline. Which reaches the bottom first?
Q9.
When a spinning ice skater pulls in her arms, her angular velocity:
Q10.
The moment of inertia of a uniform rod of mass M and length L about one end is:
Q11.
Which theorem relates the moment of inertia about an axis through the centre of mass to that about a parallel axis?
Q12.
For a body rolling without slipping on a surface, which condition must hold?
Q13.
Angular momentum L of a rotating body is given by:
Q14.
A disk has moment of inertia I about its axis. What is the moment of inertia of a ring of same mass and radius about its axis?
Q15.
Torque is defined as:
Q16.
The rotational kinetic energy of a body with moment of inertia I rotating at angular speed ω is:
Q17.
The perpendicular axis theorem applies only to:
Q18.
If a sphere rolls down without slipping, what fraction of its total KE is rotational?
Q20.
A torque does zero work on a rotating body when the force is:
Q21.
Which of the following has the largest moment of inertia for same mass M and radius R, about the central axis?
Q22.
What is the angular acceleration α if a torque of 10 N·m acts on a body with I = 5 kg·m²?
Q23.
The linear velocity of a point on a rotating body at distance r from the axis is:
Q24.
Which conservation law explains why a planet moves faster when closer to the Sun?
Q25.
A solid disc of mass 4 kg and radius 0.2 m rolls without slipping at 3 m/s along level ground. Its total kinetic energy is:
Q26.
A uniform disc of mass 2 kg and radius 0.5 m rotates about its central axis. Its moment of inertia is:
Q27.
A constant torque brings a wheel of moment of inertia 5 kg·m<sup>2</sup> from rest to 20 rad/s in 4 s. The torque applied is:
Q28.
A solid sphere and a hollow sphere have the same mass and radius. The ratio of their moments of inertia (solid : hollow) about a diameter is:
Q29.
A flywheel of moment of inertia 0.5 kg·m<sup>2</sup> rotates at 20 rad/s. Its rotational kinetic energy is:
Q30.
A solid cylinder of mass 2 kg and radius 0.1 m rolls down a 30° incline without slipping. What is its acceleration?
Q31.
A wheel of moment of inertia 2 kg·m² is rotating at 10 rad/s. A tangential force applies a torque of 4 N·m for 5 s. What is the final angular velocity?
Q32.
Using the parallel axis theorem, the MI of a rod of mass M, length L about one end is ML²/3. What is the MI about the centre?
Q33.
A torque of 20 N·m acts on a rigid body for 4 s. If the body starts from rest, what is the angular momentum after 4 s?
Q34.
A turntable rotating at 60 rpm has moment of inertia 4 kg·m². A person of mass 60 kg sits at the edge (r = 1 m). What is the new angular velocity? (Assume no friction)
Q35.
For a disk rolling without slipping at speed v, the speed of the topmost point is:
Q36.
The radius of gyration k of a body is defined by:
Q37.
A solid sphere is rotating at ω. If its radius is doubled keeping mass constant, and angular momentum is conserved, what is the new angular velocity?
Q38.
A rigid body is in rotational equilibrium. This means:
Q39.
A particle of mass m moves in a circle of radius r. The angular momentum about the centre is:
Q40.
The moment of inertia of a rectangular plate of mass M, dimensions a × b about an axis through its centre perpendicular to its plane is:
Q41.
An object rolls down without slipping. The ratio of translational KE to rotational KE for a solid disk is:
Q42.
The work done by a torque τ through an angular displacement θ is:
Q43.
A flywheel has I = 8 kg·m². It is brought to rest from 100 rad/s in 20 s. What is the braking torque?
Q44.
For the perpendicular axis theorem, if I<sub>x</sub> = I<sub>y</sub> for a symmetric disk, then I<sub>z</sub> equals:
Q45.
Two disks of equal mass are joined coaxially. Their MIs about their common axis are 3 kg·m² and 5 kg·m². What is the combined MI?
Q46.
The kinetic energy of a rolling object can be written as (1/2)mv²(1 + k²/R²) where k is radius of gyration. For a ring, k²/R² = 1. So the KE is:
Q47.
A diver tucks in during a dive. What happens to their angular velocity?
Q48.
A point mass m is attached to the end of a string and rotates in a horizontal circle of radius r. The angular momentum about the centre is L = mvr. If r is halved and v is doubled, L becomes:
Q49.
The moment of inertia of a thin ring about a diameter (not central axis) is:
Q50.
A child of mass 30 kg stands at the rim of a merry-go-round of moment of inertia 200 kg·m<sup>2</sup> and radius 2 m turning at 2 rad/s. The child walks to the centre. The new angular velocity is:
Q51.
Two masses of 3 kg and 5 kg are fixed at the ends of a light rod of length 0.8 m. The distance of the centre of mass from the 3 kg mass is:
Q52.
A uniform rod of mass M and length L is pivoted at one end and released from a horizontal position. Its angular acceleration at the instant of release is:
Q53.
A solid sphere rolls without slipping down an incline of angle θ. The minimum coefficient of friction required is:
Q54.
A disc of moment of inertia 4 kg·m<sup>2</sup> rotates at 10 rad/s. A lump of clay is dropped onto its edge, adding 1 kg·m<sup>2</sup> to the moment of inertia. The new angular velocity is:
Q55.
A wheel of moment of inertia 2 kg·m<sup>2</sup> spinning at 50 rad/s is stopped by a constant retarding torque of 5 N·m. The time taken to stop is:
Q56.
A solid cylinder of mass M and radius R is free to rotate about its horizontal axis. A string wound around it carries mass m. What is the acceleration of the hanging mass?
Q57.
A rod of length L stands vertically on a frictionless floor and falls. What is the angular velocity when it hits the floor?
Q58.
A wheel of radius R rolls without slipping. What is the acceleration of the topmost point?
Q59.
Two particles of masses m and 2m are attached to the ends of a uniform rod of mass M and length L. What is the MI about the centre of the rod?
Q60.
A spinning top (gyroscope) precesses when tilted. The precession angular velocity is:
Q61.
A ball is thrown with backspin onto a rough floor. Initially v (forward) and ωR > v. The friction force on the ball is:
Q62.
The angular momentum of a system is conserved when:
Q63.
A uniform disk of mass M and radius R has a hole of radius R/2 cut from it, centred at R/2 from the centre. What is the new moment of inertia about the disk centre?
Q64.
A solid sphere rolls without slipping up an incline, starting with translational speed v. How high does it go?
Q65.
A particle of mass m moves in a plane. Its position vector is r = (t², 3t). What is the angular momentum about the origin at t = 1?
Q66.
For a conical pendulum, the tension T in the string provides centripetal force and supports weight. The angular velocity is:
Q67.
A uniform rod of length L and mass M can rotate about one end. It is held horizontal and released. What is the velocity of the free end just as the rod becomes vertical?
Q68.
Two equal masses m are at the ends of a rod of negligible mass, length 2a. The rod rotates about its centre at ω. One mass suddenly falls off. What happens to ω?
Q69.
A horizontal disk rotating at ω has a coefficient of friction μ between it and a small block placed at distance r from centre. The block will start sliding if:
Q70.
The spin angular momentum of Earth is approximately 7 × 10³³ kg·m²/s. If Earth suddenly contracted to half its radius, its day would be:
Q71.
A disk of moment of inertia I and angular velocity ω is dropped onto another stationary disk with the same I. They eventually reach the same speed due to friction. Final ω is:
Q72.
The precession rate of a gyroscope increases if:
Q73.
A particle of mass m undergoes uniform circular motion at radius r with speed v. Its angular momentum magnitude about a point P that is at distance d from the centre (coplanar) is:
Q74.
A solid ball rolling without slipping on a curved bowl oscillates about the bottom. The effective restoring force gives period T = 2π√(7R/5g) for a bowl of radius R. This is analogous to a pendulum of effective length:
Q75.
The moment of inertia of a uniform solid sphere of mass M and radius R about a diameter is:
Q76.
The moment of inertia of a solid sphere of mass M and radius R about a tangent line is:
Q77.
For a ring rolling without slipping, the fraction of its total kinetic energy that is rotational is:
Q78.
A uniform solid disc rolls without slipping down an incline of angle θ. Its linear acceleration is:
Q79.
A skater spinning with her arms out pulls them in so her moment of inertia halves. Her rotational kinetic energy:
Q80.
Two point masses, 2 kg at the origin and 3 kg at x = 5 m, form a system. The x-coordinate of the centre of mass is:
Q81.
A solid cylinder and a hollow cylinder of the same mass and radius are released from rest at the top of the same incline. Which reaches the bottom first?
Q82.
A torque of 2 N·m acts on a disc of moment of inertia 0.5 kg·m². Its angular acceleration is:
Q83.
A force of 10 N is applied perpendicular to a wrench at 0.5 m from the pivot. The torque produced is:
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