Question

In the arrangement shown in figure the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed

• A.
• B.
• C.
• D.

Answer 1

The correct option is D


As P and Q fall down, the length l decreases at the rate of U m/s. From the figure, $l^2=b^2+y^2$
Differentiating with respect to time
$2l\times \frac{dl}{dt}=2b\times \frac{db}{dt}+2y\times \frac{dy}{dt}(As\frac{db}{dt}=0,\frac{dl}{dt}=U)$
$\Rightarrow \frac{dy}{dt}=\left(\frac{l}{y}\right)\times \frac{dl}{dt}\Rightarrow \frac{dy}{dt}=\left(\frac{1}{cos\theta }\right)\times U=\frac{U}{cos\theta }$