question_answer

In the arrangement shown in the figure 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)               \[2U\cos \theta \]                             

B)  \[U/\cos \theta \]

C)  \[2U/\cos \theta \]       

D)  \[U\cos \theta \]

Correct Answer: B

Solution :

\[{{l}^{2}}={{a}^{2}}+{{y}^{2}}\]                         \[2l.\frac{dl}{dt}\,=0+2y\,\frac{dy}{dt}\] (a is constant) \[-\frac{dy}{dx}=\frac{l}{y}\,\left( -\frac{dl}{dt} \right)\] \[or\,\,+{{v}_{M}}\,=\frac{1}{\cos \theta }\,(U)\,=\frac{U}{\cos \theta }\]