First slide

Constraints

Question

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

Moderate

A

2Ucosq
B

Ucosq
C

2U/cosq
D

U/cosq

Solution

As P and Q move down, the length l decreases at the rate of U m/s.
From figure (1), $l^{2} = b^{2} + y^{2}$
Differentiating with respect to time
$2 l \frac{dl}{dt} = 2 y \frac{dy}{dt}$
$∴ \frac{dy}{dt} = \frac{ldl}{ydt} = \frac{1}{\cos θ} \cdot \frac{dl}{dt} = \frac{U}{\cos θ}$ .

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