Figure shows a small block of mass m kept at the left end of a larger block of mass M and length l. The system canslide on a horizontal road. The system is started towards right with an initia velocity v. The friction coefficient between the road and the bigger block is `mu` and that between the block is `mu/2`. Find the time elapsed before the smaller blocks separates from the bigger block.

Answer

D

Explanation

Let `a_1 and a_2` and the acelerations of m and M respectively.
Here `a_1gta_2` so that moves on M. Suppose after time t, m is seperted from M.
In this time , m covers `vt+1/2 a_1t^2 and S_v=vt+1/2a_2t^2`
For m to separate from M
`vt+1/2a_1t^2=vt+1/2a_2t^2+1`...ii
Again from the free body diagram
`ma_1+mu/2R=0`
`rarr ma_1=-(mu/2)mg=(mu/2)mxx10`
`rarr a_1=-5mu`

Again `Ma_2+mu(M+m)g-(mu/2)mg=0`
`rarr 2Ma_2=mumg-2muMg-2mumg`
`rarr a_2=(-mumg-2muMg)/(2M)`

Putting values of `a_1`
and `a_2in equation
i. we get,
`t sqrt((4Ml)/((M+m)mug)`