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.

Figure shows a small block of mass m kept at the left end of a larger

1.	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» Solution :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 fromM. 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)`