Question

A rolling sphere collides with a cube of equal mass. Surface is frictionless. Radius of sphere is 1 cm and its initial angular speed is 1 radian per second.

If side of cube is 2 cm and collision is elastic, then after collision,

(a) ω_sphere = 0 and v_cube = 0.01 ms⁻¹

(b) ω_sphere = 1\(\frac{rad}{s}\) and v_cube = 0.01 ms⁻¹

(c) ω_sphere = 0 and v_cube = 0

(d) ω_sphere = 1\(\frac{rad}{s}\) and v_cube = 1 ms⁻¹

Answer 1

Correct option is (b) ω_sphere = 1\(\frac{rad}{s}\) and v_cube = 0.01 ms⁻¹

Before collision, velocity of translation of sphere

v_cube = rω = 1 cms⁻¹ = 0.01 ms⁻¹

As collision is elastic, translational kinetic energy of sphere is transferred to the cube but its rotational kinetic energy remains constant.