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. $2u\cos \theta$
• B. $u/\cos \theta$
• C. $2u/\cos \theta$
• D. $u\cos \theta$

Answer 1

The correct option is B $u/\cos \theta$

Hence,

option $\left(B\right)$ is correct answer.

Let the speed of mass $M$ be v

The point on thread just connected to mass M will also have the same velocity.

The component of the v along the thread is $vcos\theta$. That means any point on the thread must be moving with speed $vcos\theta$.

As it is given that thread is moving with velocity $u$.

That means

$vcos\theta =u$

$\Rightarrow v=\frac{u}{\cos \theta }$