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A plank of mass 4m is placed on a smooth...

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 :

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))`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`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`
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