Question

In the arrangement shown in the figure, the ends $P$ and $Q$ of an inextensible string move downwards with uniform speed $u$. Pulleys $A$ and $B$ are fixed. What is the speed with which mass $M$ moves up?

• A. $2u\cos \theta$
• B. $u\cos \theta$
• C. $\frac{2u}{\cos \theta }$
• D. $\frac{u}{\cos \theta }$

Answer 1

The correct option is D $\frac{u}{\cos \theta }$


Let the velocity of block of mass $M$ be $v$ as shown in the figure.
From constrained condition, along the string the net velocity should be zero.
$\Rightarrow v\cos \theta =u$
$v=\frac{u}{\cos \theta }$

Hence the speed with which mass M will move up is $\frac{u}{\cos \theta }$