A sufficiently long plane of mass `4kg` is placed on a smooth horizontal surfaces A small block of mass `2kg` is placed over the plank and is beging acted upon by a time verying horizontal force `F = (0.5t)` where f is in newton and t is in second as shown in figure .The coefficient of friction slipping the plank and the block is given is `mu_(s) = mu_(k) = mu` time `t = 12s` the relative slipping between the plank and the block is just likely to accor

The average acceleration of the plank in the time interval `0 to 15s` in the figure will be

Options

A. `0.20ms^(-2)`
B. `0.30ms^(-2)`
C. `0.40ms^(-2)`
D. `0.60ms^(-2)`

Answer

d

Explanation

`(1)/(2)= (M+m)(dv)/(dt)`
`int_(0)^(v) dv = int_(0)^(12)(t)/(2(M+m))dt rArr v = 6ms^(-1)`
After `12s` up to `15s for 3s` the acceleration of plank will be
`a= (0.2 xx 2 xx10)/(4) = 1ms^(-1)`
`v^(1)= 6+3xx1 = 9ms^(-1) a_(av)= (v^(1) - 0)/(15) = (9)/(15)= 0.6ms^(-2)`