Question

In the arrangement shown in the figure, the ends P and Q of an un-stretchable 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. $\frac{U}{\cos \theta }$
• C. $\frac{2U}{\cos \theta }$
• D. $U\cos \theta$

Answer 1

The correct option is B $\frac{U}{\cos \theta }$

Let speed of mass $M$ be the $V$

the point on the thread just connected to mass $M$ will have the same velocity

the component $v$ along the thread is $vcos\theta$

the point of thread is moving with the speed of $vcos\theta$ as it is given in the thread moving with the velocity $u$

$vcos\theta$ is equal to$u$

$V=\frac{u}{cos\theta }$