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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
`(1)/(2) mv^(2)= (1)/(2) kx^(2) + f_(k) x`
`rArr (1)/(2) xx 2 xx 16= (1)/(2) kx^(2)+ 15x`
`rArr 16= (1)/(2) xx 10,000 x^(2)+ 15x`
`rArr 5000x^(2)+ 15x- 16= 0`
`x= (-15 pm sqrt(225 +4 xx 16 xx 5000))/(10000)` x= 5.5cm
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