In the figure, the ball B is released from rest when the spring is in natural length. For the block A of mass 2m to leave contact with the ground at some instant the minimum mass of B must be

Options

A. 2m
B. m
C. `(m)/(2)`
D. `(m)/(4)`

Answer

D

Explanation

Using conservation of momentum,
`2mV = sqrt(m^(2)v^(2)+m^(2)v^(2))`
`2mV=sqrt(2m^(2)v^(2))`
`V=(v)/(sqrt(2))`]
Energy released in explosion `=2xx(1)/(2)mv^(2)+(1)/(2)xx2mxx(v^(2))/(2)=(3)/(2)mv^(2)`