A small block of mass m is plced over a long plank of mass M the coefficient of friction between then is `mu` ground is smooth At `t = 0` m is given a velocity `v_(1)` and M a velocity `v_(2) (gtv_(1))` as shown in figure After this M is maintained at constant celeration `a(ltmu g)`

Initially there will be some relative motion between the block and the plank ,but after some time relative motion will cease and velocities of both will become
Find the forward force acting on the plank before after `t_(0)` respectively.

Options

A. `Ma,(M + m)a`
B. `mu mg + Ma,(M + m)a`
C. ` mu M g +ma + Ma`
D. `(M + m)a,mu mg +Ma`

Answer

b

Explanation

For `t lt t_(0):`

Let `F` be the forward force then
`F - ma = Ma rArr F = (m +M)a`
For `t gt t_(0)`:
Let `F` be the formward force, then
`F - ma = Ma rArr F =(m+M) a`