Question

At a given instant, block A is moving upwards with velocity of $5m/s$, what is velocity of block B at that instant? Assume that the strings are inextensible and pulleys are frictionless.

• A. $15m/s\downarrow$
• B. $15m/s\uparrow$
• C. $10m/s\downarrow$
• D. $5m/s\uparrow$

Answer 1

The correct option is A $15m/s\downarrow$


Since the string is inextensible, length of the string remains constant. Let $l_1$, $l_2$, $l_3$ and $l_4$ are the intercepts of the string.
$l_1+l_2+l_3+l_4=\text{constant}$
Differentiating the above equation w.r.t time $t$, we get equation in terms of velocity i.e.
$\Rightarrow -V_A-V_A-V_A+V_B=0$ (Taking upward velocity to be negative and downward positive)
$\Rightarrow -5-5-5+V_B=0$
$V_B=15m/s\downarrow$