A solid sphere of mass 2 kg is rolling on a frictionless horizontal surface with velocity 6 m s - 1 . It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (Force constant of the spring = 36 N m - 1 ).

Step-by-step solution

Kinetic energy of rolling solid sphere = 1 2 m V 2 + 1 2 I ω 2 = 1 2 m V 2 + 1 2 × 2 5 m r 2 ω 2 = 1 2 m V 2 + 1 5 m V 2 = 7 10 m V 2 The potential energy of the spring on maximum compression x = 1 2 k x 2 ∴         1 2 k x 2 = 7 10 m V 2 x 2 = 14 10 m V 2 k = 14 10 × 2 6 2 36     = 2.8 x = 2.8  m