Question

Find the velocity of block $C$ i.e. $V_C$ in the shown figure.

• A. $V_C=6\text{m/s}$, downward
• B. $V_C=4\text{m/s}$, upward
• C. $V_C=8\text{m/s}$, upward
• D. $V_C=10\text{m/s}$, downward

Answer 1

The correct option is C $V_C=8\text{m/s}$, upward

Let us assume that the velocity of block $C$ and pulley $P_3$ i.e. $V_{P3}$ be upward respectively and taking upward positive we have

From string constraints
$V_B\cos {60}^{\circ }=V_{P2}\Rightarrow V_{P2}=6\cos {60}^{\circ }=3\text{m/s}$
For pulley $P_3:$
$V_{P3}=\frac{V_D+V_A}{2}=\frac{0-4}{2}=-2\text{m/s}$
Again for pulley $P_2:$
$V_{P2}=\frac{V_C+V_{P3}}{2}=\frac{V_C-2}{2}$
$\Rightarrow 3=\frac{V_C-2}{2}\Rightarrow V_C=8\text{m/s}$
Hence, the velocity of block $C$ is $V_C=8\text{m/s}$, upward.