This page covers CAPF AC System of Particles & Rotational Motion with complete concept notes, 18 graded practice MCQs, key points and exam-specific tips. Free to study.
18graded MCQs · easy to hard · full solution & trap analysis
A uniform rod of mass 2 kg and length 4 m is rotating about its center. If the moment of inertia about the center is 2.67 kg·m², what is the radius of gyration of the rod about its center?
A system consists of three point masses: 2 kg at (0, 0), 3 kg at (2, 0), and 5 kg at (2, 2). The y-coordinate of the center of mass is:
A torque of 12 N·m is applied to a wheel with moment of inertia 3 kg·m². If the wheel starts from rest, what is the angular acceleration?
Two particles of mass 3 kg and 5 kg are separated by 2 m. The center of mass of the system is at a distance of x m from the 3 kg mass. What is the value of x?
A solid disc of mass 4 kg and radius 0.5 m rotates with angular velocity 20 rad/s. What is its rotational kinetic energy? (Use I = ½MR² for disc)
Two particles of equal mass m are placed at the corners of a square of side a. What is the moment of inertia of the system about an axis passing through one corner and perpendicular to the plane of the square?
A solid sphere of mass 5 kg and radius 0.2 m rotates about a diameter with angular velocity ω = 4 rad/s. Calculate its rotational kinetic energy. (Use I = (2/5)MR²)
Three point masses of 1 kg each are fixed at the vertices of an equilateral triangle of side 2 m. What is the moment of inertia of the system about an axis passing through one vertex and perpendicular to the plane?
Two blocks of mass 2 kg and 3 kg are connected by a light inextensible string over a pulley (treat as a point mass). If the system is released from rest, what is the magnitude of acceleration of the blocks? (Use g = 10 m/s², neglect pulley mass and friction)
A uniform disc of mass M = 2 kg and radius R = 0.4 m is rotating about its central axis. If its angular velocity increases from 0 to 10 rad/s in 5 seconds, calculate the angular acceleration.
A wheel of moment of inertia I = 0.5 kg·m² is rotating at 20 rad/s. A constant retarding torque of 2 N·m is applied. How long does it take to stop?
A uniform rod of length L = 0.6 m and mass M = 3 kg is pivoted at one end. What is its moment of inertia about the pivot point? (Use I = (1/3)ML²)
A system of two particles of masses 2 kg and 3 kg are separated by 0.5 m. The centre of mass is located at a distance of 0.3 m from the 3 kg mass. Find the distance of centre of mass from the 2 kg mass.
A rigid body rotates about a fixed axis with angular acceleration α = 2 rad/s². If the moment of inertia is I = 4 kg·m², what is the net torque acting on the body?
A uniform rod of mass 2 kg and length 4 m rotates about its center. If the moment of inertia about the center is 2.67 kg·m², calculate the radius of gyration of the rod about its center.
Two particles of masses 3 kg and 5 kg are separated by 2 m. Their center of mass lies at a distance from the 3 kg mass of:
A disc of mass 4 kg and radius 0.5 m rotates with angular velocity 10 rad/s. If another disc of mass 2 kg and radius 0.5 m is placed coaxially on it and friction causes them to rotate together, find the final common angular velocity.
A system consists of three point masses: 1 kg at origin, 2 kg at (2, 0) m, and 3 kg at (0, 2) m. The y-coordinate of the center of mass is: