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

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

A

`5.5 cm`

B

`2.5 cm`

C

`11.0 cm`

D

`8.5 cm`

Text Solution

Verified by Experts

The correct Answer is:
A
`W.D_(f) = K_(f) + U_(f) - K_(i) - U_(i)`
`rArr - f.x = (1)/(2)kx^(2) + 0 - (1)/(2)mv^(2) - 0`
`rArr - 15x = 5000 x^(2) - 16 = 0`
`rArr 5000 x^(2) + 15x - 16 = 0 rArr x = 5.5 cm`
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