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$A bead C$ can move freely on a horizontal rod. The bead is connected by blocks $B and D$ by a string as shown in the figure. If the velocity of $B is v$ . The velocity of block $D$ is $4 v / x$ , find the value of $x$

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answer is A.

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Detailed Solution

Concept : along the length of string velocity component is same for all the points on string.

$v_{B} = v_{C} \cos 53^{0} \dots \dots (1) v_{C} \cos 37^{0} = v_{D} from eqns. (1) and (2) we get v_{D} = \frac{v_{B} \cos 37^{0}}{\cos 53^{0}} = \frac{v_{B} (4 / 5)}{(3 / 5)}; v_{D} = \frac{4}{3} v$

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