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In the arrangement shown, blocks $A$ and $B$ connected with an inextensible string move with velocities $v_{1}$ and $v_{2}$ along horizontal direction. The ratio of $\frac{v_{2}}{ν_{1}}$ is

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$\frac{\sin α}{\sin β}$

$\frac{\sin β}{\sin α}$

$\frac{\cos β}{\cos α}$

$\frac{\cos α}{\cos β}$

answer is D.

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Detailed Solution

$- T \cos β V_{2} = T \cos α V_{1} = 0 \cos β V_{2} = \cos α V_{1}; \frac{V_{2}}{V_{1}} = \frac{\cos α}{\cos β}$

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