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
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
$2U\cos \theta $
$U\cos \theta $
$\frac{{2U}}{{\cos \theta }}$
$\frac{U}{{\cos \theta }}$
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
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
$2l \times \frac{{dl}}{{dt}} = 2b \times \frac{{db}}{{dt}} + 2y \times \frac{{dy}}{{dt}}$ $\left( {{\rm{As \,\,}}\frac{{db}}{{dt}} = 0,\frac{{dl}}{{dt}} = U} \right)$
$⇒$ $\frac{{dy}}{{dt}} = \left( {\frac{l}{y}} \right) \times \frac{{dl}}{{dt}}$ $ \Rightarrow \frac{{dy}}{{dt}} = \left( {\frac{1}{{\cos \theta }}} \right) \times U = \frac{U}{{\cos \theta }}$
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