Question

In the figure shown, neglect the masses of the pulley and also neglect friction, then choose the correct option.

• A. Tension in the string connected to block is $\frac{mg}{2}$
• B. Acceleration of block is ${}^{\prime }{g}^{\prime }$ downward
• C. Acceleration of pulley $P_2$ is ${}^{\prime }{g}^{\prime }$ upward
  
• D. Acceleration of pulley $P_3$ is $\frac{{}^{\prime }{g}^{\prime }}{2}$downward

Answer 1

The correct option is B Acceleration of block is ${}^{\prime }{g}^{\prime }$ downward

Let us draw the FBD first

Since the same string is connected from $P_1,P_2$ and $P_3$ , the tension will be equal, let's say $T$.
Now, from the FBD, net force on the pulley $P_2$ and $P_3$ will be zero (Pulleys are massless). Also, on $P_1$

net force will be $T$ upwards, but, for massless system net force should be zero i.e. $F_{net}=0$.
So, $T=0$
So, force on mass $m,$ is only due to gravity.
Hence, the tension in the string is zero and block is falling freely.