Question

Seven pulleys are connected with the help of $3$ light strings as shown in the figure. Consider $P_3,P_4,P_5$ as light pulleys and pulleys $P_6$ and $P_7$ have masses $m$ each. For this arrangement mark the correct statement(s):

• A. Tension in the string connecting $P_1,P3$ and $P_4$ is zero
• B. Tension in the string connecting $P_1,P_3$ and $P_4$ is $\frac{mg}{3}$
• C. Tension in all the 3 strings are same and equal to zero
• D. Acceleration of $P_6$ is $g$ downward and that of $P_7$ is $g$ upward

Answer 1

Answer: (A), (C)

Tension in the string connecting $P_1,P3$ and $P_4$ is zero
Tension in all the 3 strings are same and equal to zero

Let tension, in $3$ strings be $T_1$, $T_2$ and $T_3$ respectively
For pulley $P_3:2T_1-T_1=0\times a$ $\Rightarrow$ $T_1=0$
For pulley $P_4:2T_1-T_2=0$ $\Rightarrow$ $T_2=0$
For pulley $P_5:2T_2-T_3=0$ $T_2=T_3=0$