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).

Options

A. `sqrt(14) `m
B. `sqrt(2.8)` m
C. `sqrt(1.4)` m
D. `sqrt(0.7)` m

Answer

B

Explanation

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