Question

In the arrangement shown in figure the ends P and Q of an inextensible string move downwards with uniform speed u. Pulleys A and B are fixed. The mass M moves upwards with a speed
(a) 2u cos θ
(b) u/cos θ
(c) 2u/cos θ
(d) u cos θ
Figure

Answer 1

(b) $v=\frac{u}{\cos \left(\theta \right)}$



Along the string, the velocity of each object is the same.
$$\begin{gathered} 2v\cos \left(\theta \right)=2u \\ v=\frac{u}{\cos \left(\theta \right)} \end{gathered}$$