Question

At a given instant, block $A$ is moving with velocity of $5\text{m/s}$ upwards. What is the velocity of block $B$ at that time?

• A. $15\text{m/s}$ (Downward)
• B. $15\text{m/s}$ (Upward)
• C. $10\text{m/s}$ (Downward)
• D. $10\text{m/s}$ (Upward)

Answer 1

The correct option is A $15\text{m/s}$ (Downward)

Let divide the rope into three parts $l_1,l_2,l_3$ as shown in figure. Assume block B is moving downward.

$l_1+2l_2+l_3=$ constant
Now, differentiating the above equation with respect to time, we get
$-v_A-2v_P+v_B=0$
Here, $v_P=$ velocity of pulley $=v_A$
$\Rightarrow v_B=3v_A$
$=15m/s$ (downward)