First slide

Constraints

Question

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

Moderate

A

$2 U \cos θ$
B

$U \cos θ$
C

$\frac{2 U}{\cos θ}$
D

$\frac{U}{\cos θ}$

Solution

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

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App