When the spring is compressed to maximum , what fraction of incidetn the kinetic energy is stored in spring ?

Options

A. `(1)/(4)`
B. `(1)/(2)`
C. `(3)/(4)`
D. `(1)/(3)`

Answer

C

Explanation

When the spring is compressed to the maximum , both the ball and the spring have same velocity.
Momentum conservation :
` m u = ( m + 3 m) V rArr V = (u)/(4)`
Energy conservation :
`(1)/(2) m u^(2) = (1)/(2) ( m + 3m) V^(2) + (1)/(2) k x^(2)`
` = (1)/(2) xx 4m (u^(2))/(16) + (1)/(2) kx^(2)`
`(1)/(2) k x^(2) = (3)/(8) m u^(2)`
Fraction of incident `K.E.` stored in the spring is
`((1)/(2) kx^(2))/((1)/(2) m u^(2)) = ((3)/(8))/(( 1)/(2))= (3)/(4)`