Question

37. A sphere of radius 2m rolls on a floor the
acceleration of the centre of mass of sphere is 4 m/s2
Angular acceleration a about its centre of mass is
4 m/s²
(com
>
O
(1) 2 rad/s2
(3) 3 rad/s2
(2) 4 rad/s2
(4) 1 rad/s2
kash Tower, 8, Pusa Road, New Delhi-110005 Ph.011-47623456​

Answer 1

answer : option (3) 3 rad/s²

explanation : we know, moment of inertia of hollow sphere about centre of mass , I = 2/3 Mr²

now, torque = angular acceleration × momentum of inertia

or, F × r = α × I

here, α is angular acceleration about centre of mass of sphere.

here, F = Ma = M(4 m/s²)

r = 2m , I = 2/3 Mr² = 2/3 M(2m)²

so, M(4m/s²) × (2m) = α × 2/3 M(2m)²

or, 8 = α × 2/3 × 4

or, α = 3 rad/s²

hence, angular acceleration about centre of mass is 3 rad/s²