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 can slide on a horizontal road. The system is started towards right with an intial velocity v. The friction coefficient between the road and the bigger block is µ and that between the blocks is µ/2.Find the time elapsed before the smaller block separates from the bigger block.

Dear jayesh

N1=mg

N2=(m+m)g

a1=-μ/2 N1/m

   =-μg/2

a2=(μN1/2 -μN2)/M

    =(μmg/2 -μ(m+m)g)/M

initial velocity of smaller block with respect to biggere =v-v =0

acceleration of smaller block w.r.t bigger = a1-a2

so smaller block sepeate

 S=l =0*t +1/2 (a1-a2) t² 

t² =2l/(a1-a2)

put value of a1 and a2

and find t

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Approved

Dear Student,
Please find below the solution to your problem.


N1=mg
N2=(m+m)g
a1=-μ/2 N1/m
=-μg/2
a2=(μN1/2 -μN2)/M
=(μmg/2 -μ(m+m)g)/M
initial velocity of smaller block with respect to biggere =v-v =0
acceleration of smaller block w.r.t bigger = a1-a2
so smaller block sepeate
S=l =0*t +1/2 (a1-a2) t2
t2 =2l/(a1-a2)
put value of a1 and a2
and find t

Thanks and Regards