Question

Three blocks $A,B$ and $C$ of mass $m$ each are arranged in pulley mass system as shown. Coefficient of friction between block $A$ and horizontal surface is equal to $0.5$ and a force $P$ acts on $‘A^{\prime }$ in the direction shown. The value of $\frac{P}{mg}$ so that block $‘C^{\prime }$ doesn’t move is

Answer 1

By string constraints,
If $C$ doesn't move then $a_A=4a_B$ ... (i)
$P-T-\mu mg=m4a_B$ ... (ii)
$4T-mg=m{a}_B$ ... (iii)
Also $2T=mg$ (balancing force on $C$)
$\therefore \frac{p}{mg}=5$