Consider the situation shown in figure. The block B moves on a frictionless surface, while the coefficient of friction between A and the surface on which it moves is 0.2. Find the acceleration with which the masses move and also the tension in the strings. (Take $g=10 \mathrm{m}/{\mathrm{s}}^2$ ).

 Solution Let a be the acceleration with which the masses move and $T_1$ and $T_2$be the tensions in left and right strings. Friction on mass A is $\mu mg=8 \mathrm{N}$. Then equations of motion of masses A, B and C are

For mass A

$T_1-8=4a$                                               ……………….(i)

$T_2=8a$                                                 ………………..(ii)

$200-T_1-T_2=20a$                                 …………………..(iii)

For mass B

For mass C

Adding the above three equations, we get \(32 a=192\)

or

$a=6 \mathrm{m}/{\mathrm{s}}^2$

From Equations (i) and (ii), we have

$T_2=48 \mathrm{N}$

and

$T_1=32 \mathrm{N}$