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A plank having mass M is placed on smoot...


A plank having mass M is placed on smooth horizontal surface. Block of mass m is placed on it coefficient of friction between block and plank is `mu_(0)+kx`, where k is constant and x is relative displacement between block and plank. A force F is applied on block where `F=at`, where a=10 t is in second. find `t_(0)` when relative motion will occur between block and plank.

A

`mu_(0)M+(mu_(0)M^(2))/(m)`

B

`mu_(0)m+(mu_(0)M^(2))/(m)`

C

`mu_(0)m+(mu_(0)m^(2))/(M)`

D

`mu_(0)M+(mu_(0)m^(2))/(M)`

Text Solution

Verified by Experts

The correct Answer is:
C

Let at time `t_(0)` relative motion will occur
`mu_(0)mg=Ma` ..(1)
`10t_(0)-mu_(0)mg=ma` …(2)
From (1) and (2)
`t_(0)=mu_(0)m+(mu_(0)m^(2))/(M)`
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