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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 10,000 N/m. The spring compresses by :

A

2.5 cm

B

11.0 cm

C

8.5 cm

D

5.5 cm

Text Solution

Verified by Experts

The correct Answer is:
d
Here Total K.E.=P.E. of the spring + Work done against friction.
`:. 1/2mv^2=1/2kx^2+F_kxxx`
`1/2xx2xx(4)^2=1/2xx10,000x^2+15 x`
`32=10,000x^2+30 x`
`:. 10,000x^2+30 x-32=0`
or `x=(-30pmsqrt(900+4xx10,000xx32))/(20,000)`
=`(-30pm1132)/(20,000)=(1102)/(20,000)xx100 cm`
implies 5.5 cm
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