Physics

Session Rotational Mechanics -7

Session Objectives

Session Objective 1.Problems

Class Test

Class Exercise - 1 A wheel of mass 2 kg having practically all the mass concentrated along the circumference of a circle of radius 20 cm is rotating on its axis with an angular velocity of 100 rad/s. The rotational kinetic energy of the wheel is (a)4 J(b) 70 J (c) 400 J(d) 800 J

Solution Hence, answer is (c).

Class Exercise - 2 A rod of length L is hinged from one end. It is brought to the horizontal position and released. The angular velocity of the rod when it is in vertical position is

Solution Loss in potential energy = Gain in kinetic energy

Solution contd.. Hence, answer is (b).

Class Exercise - 3 The moment of inertia of a square plate about one of its diagonal is (Assume to be the side of the square and mass M)

Solution MI of a square plate about an axis passing through its centre and perpendicular to its plane is I 0 = 2I D Hence, answer is (b).

Class Exercise - 4 A uniform disc of radius R and mass M is mounted on an axle as shown in the figure. A light cord is wrapped around the rim of the wheel and a downward pull T is exerted on the cord. The angular acceleration of the wheel is

Solution Applying torque equation, torque of tension about O = TR Hence, answer is (a).

Class Exercise - 5 A particle of mass m is released from rest at A, falling parallel to y-axis. The torque acting on the particle with respect to origin and angular momentum at any time with respect to origin is (a)mgb and mgt(b) mgt and mg (c) mgb and mgbt(d) mgt and mgbt

Solution Angular momentum = Linear momentum × Perpendicular distance from the axis Velocity after time t of falling = gt L = mgt × b L = mgbt … (ii) Momentum = mgt Hence, answer is (c).

Class Exercise - 6 The ratio of the radius of gyration of a circular disc and a circular ring of the same mass and radius about a tangential axis parallel to the plane is (a)6 : 5(b) 1 : 2 (c) 5 : 6(d) None of these

Solution M.I. of circular disc about tangential axis by theorem of parallel axis is M.I. of ring about tangential axis by theorem of parallel axis is Hence, answer is (d).

Class Exercise - 7 The moment of inertia of a cylinder of radius a mass M and height h about an axis parallel to the axis of the cylinder and distant b from the centre is

Solution According to theorem of parallel axis, Hence, answer is (d).

Thank you