Question

Find the velocity of the hanging block if the velocities of the free ends of the rope are as indicated in the figure. Assume that the pulleys are frictionless and string is inextensible.

• A. $3/2m/s\uparrow$
• B. $3/2m/s\downarrow$
• C. $1/2m/s\uparrow$
• D. $1/2m/s\downarrow$

Answer 1

The correct option is A $3/2m/s\uparrow$

Since the string is inextensible, length of the string remains constant. $l_1$, $l_2$, $l_3$ and $l_4$ are the intercepts of the string.
$l_1+l_2+l_3+l_4=\text{constant}$
Differentiating w.r.t time, we get the equation in the form of velocity i.e.
${\dot{l}}_1+{\dot{l}}_2+{\dot{l}}_3+{\dot{l}}_4=0$
Assuming velocity of the intercepts whose length is increasing to be positive and velocity of block be $v_B$
$\Rightarrow +2-v_B-v_B+1=0$
$\Rightarrow v_B=3/2m/s\uparrow$