Question

Velocities of blocks $A,B$ and pulley $P_2$ are shown in the figure given below, then

• A. Velocity of pulley $P_1$ will be $5\text{m/s}$ downwards.
• B. Velocity of block $C$ will be $25\text{m/s}$ upwards.
• C. Velocity of pulley $P_1$ will be $5\text{m/s}$ upwards.
• D. Velocity of block $C$ will be $15\text{m/s}$ downwards.

Answer 1

Answer: (A), (B)

The correct options are
A Velocity of pulley $P_1$ will be $5\text{m/s}$ downwards.
B Velocity of block $C$ will be $25\text{m/s}$ upwards.

Assuming vertically upward direction as $+ve$,
Velocity of pulley $P_1$,
$V_{P_1}=\frac{V_A+V_B}{2}=\frac{(-20)+10}{2}$
$\Rightarrow V_{P_1}=-5\text{m/s}$
($-ve$ sign means $V_{P_1}$ is in downward direction)

Similarly, velocity of pulley $P_2$
$V_{P_2}=\frac{V_{P_1}+V_C}{2}$
$+10=\frac{(-5)+V_C}{2}$
$\Rightarrow V_C=25\text{m/s}$
$\therefore$Block $C$ will be moving with velocity $25\text{m/s}$, upwards.