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Q.

A rod can freely rotate in vertical plane about the hinge at its bottom. Two strings tie the top of the rod with blocks $A$ and $B$ as shown in the figure. At the instant shown, the rod is vertical and the speed of block $A$ is $u = 1 m / s$ downwards. Find the speed of block $B$ in $m / s .$

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Detailed Solution

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Let the magnitude of velocity of top of the rod be $V_{R}$ towards left and the speed of block $B$ be $V .$
$l_{1} + l_{2} = constant ∴ \frac{d l_{1}}{d t} + \frac{d l_{2}}{d t} = 0 \Rightarrow u - V_{R} \cos 60 ° = 0 ......... (1)$
$l_{3} + l_{4} = constant ∴ \frac{d l_{3}}{d t} + \frac{d l_{4}}{d t} = 0 \Rightarrow V_{R} \cos 30 ° - V = 0 ......... (2)$
Solving (1) & (2)
$V = \sqrt{3} u m / s$

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A rod can freely rotate in vertical plane about the hinge at its bottom. Two strings tie the top of the rod with blocks A and B as shown in the figure. At the instant shown, the rod is vertical and the speed of block A is u=1 m/s downwards. Find the speed of block B in m/s.