A plank of mass 4m is placed on a smooth horizontal surface and a spring of force constant k is attached to the plank, whose other end is fixed on a block of mass m placed over tha plank. All surface are smooth. A bullet of mass m moving with horizontal velocity u strikes the block and gets embeded in it. Choose the correct option for subsequent motion :

Options

A. velocity of plane when spring gets compressed to maximum is `(u)/(6)`
B. the maximum compression in the spring is `sqrt((m)/(3k))u`
C. the bullet will have velocity relative to plank at the instant of maximum compression
D. the force exerted by spring on plank will reach a maximum of `sqrt((m u^(2))/(6k))`

Answer

A, B

Explanation

`m u=6mV`
`V=(u)/(6),(1)/(2)2m(u//2)^(2)=(1)/(2)(m+m+4m)V^(2)+(1)/(2)kx^(2)`
`rArr x=sqrt((m)/(3K))u`