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
Draw the velocity of block as a function of time.

Options

A.
B.
C.
D.

Answer

a

Explanation

For `t lt t_(0)`
velocity of block at any time `v_(b) = v_(1)+ mu gt` stope of graph is `mu g` velocity of block at`t = t_(0): = v_(1) + mu gt_(0)`
or `t lt t_(0)`
velocity of block at any time `v_(b) = v_(1)+ (mg - a)t_(0) +at`
Slope of graph will decrease hence correct graph is (a)