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A box of mass m is initially at rest on ...

A box of mass m is initially at rest on a horizontal surface. A constant horizontal force of mg/2 is applied to the box directed to the right. The coefficient of friction of the surface changes with the distance pushed as `mu=mu_(0)x` where x is the distance fr4om the initial location . For what distance is the box pushed until it comes to rest again?

A

`(2)/(mu_(0))`

B

`(1)/(mu_(0))`

C

`(1)/(2mu_(0))`

D

`(1)/(4mu_(0))`

Text Solution

Verified by Experts

The correct Answer is:
B
Net change in kinetic energy =0 `rArr` net work W=0

`w=intdW=intFdx-intmuNdx=(mg)/(2)xx0mg1_(0)int_(0)^(x)xdx=0rArrx=(1)/(mu_(0))`
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