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

A solid sphere of mass 2 kg is rolling on a frictional horizontal surf

1.	A solid sphere of mass 2 kg is rolling on a frictional horizontal surface with velocity 6 m/s. It collides on the free end of an ideal spring whose other end in fixed. The maximum compression produced in the spring will be (Force constant of the spring is 36 N/m).
Answer» `sqrt(14) `m `sqrt(2.8)` m `sqrt(1.4)` m `sqrt(0.7)` m Solution :Kinetic energy of rolling SOLID sphere `= (1)/(2) mv^(2) + (1)/(2) I OMEGA^(2) = (1)/(2) mv^(2) + (1)/(2) xx (2)/(5)mr^(2) omega^(2) = (1)/(2) mv^(2) + (1)/(5) mv^(2)` `= (7)/(10) mv^(2) = (7)/(10) xx 2 xx (6)^(2) = (7)/(10) xx 2 xx 36 = (252)/(5)` The potential energy of the spring of MAXIMUM compression X , `= (1)/(2) kx^(2) or (1)/(2) kx^(2) = (252)/(5) , kx^(2) = (252 xx 2)/(5)` `x^(2) = (252 xx 2)/(5 xx 36) = 2.8 or x = sqrt(2.8)` m