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A 2kg block slides on a horizontal floor...

A `2kg` block slides on a horizontal floor with the a speed of `4m//s` it strikes a uncompressed spring , and compresses it till the block is motionless . The kinetic friction force is compresses is `15 N` and spring constant is `10000 N//m` . The spring by

A

`2.5`

B

`11.0`

C

`8.5`

D

`5.5`

Text Solution

Verified by Experts

The correct Answer is:
D
Let the spring be compressed by `x`.
Loss in `KE` of block
= Gain in `PE` of spring + Work done against friction
`rArr (1)/(2) xx 2 xx4^(2) =(1)/(2) 1000 x^(2) + 15 x`
On solving, we get `x = 5.5 cm`.
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