Question

Find the velocity of block $B$ i.e. $v_B$ in the shown figure.

• A. $v_B=10v$, downward
• B. $v_B=12v$, upward
• C. $v_B=\frac{12v}{5}$, upward
• D. $v_B=8v$, downward

Answer 1

The correct option is B $v_B=12v$, upward

Let the velocity of block $B$ be $v_B$ and the velocity of pulley connected to block $B$ and $C$ be $v_P$ respectively upward, and taking upward positive we have


As we know that, the string's end attached to the fixed pulley will have zero velocity. So, considering the points $1$ to $6$ in the figure, we have
$v+v+v+v+v-v_P=0\Rightarrow v_P=5v$
Also, from pulley relation we have
$v_P=\frac{v_B+v_C}{2}\Rightarrow 5v=\frac{v_B-2v}{2}$
$\Rightarrow v_B=12v$
Hence, the velocity of block $B$ is $v_B=12v$, upward.