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.

Options

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)`

Answer

C

Explanation

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)`