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Q.

Two particles P and Q of masses m and 2 m are connected by a light string passing over a light pulley as shown in figure. Initially the particles are held in position by an external agent. At an instant of time, the particles are released simultaneously. Then the speed of each particle when their vertical separation is h will be

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a

$\sqrt{\frac{2 g h}{3}}$

b

$\sqrt{\frac{g h}{6}}$

c

$\sqrt{\frac{g h}{3}}$

d

$\sqrt{2 g h}$

answer is C.

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Detailed Solution

$Acceleration of the masses are a = \frac{(2 m - m)}{(2 m + m)} g = \frac{g}{3} initial relative velocity between them is zero and final relative distance between them is h and relative acceleration between them is 2 a so v is their relative velocity then v = \sqrt{2 ah} = \sqrt{\frac{2 gh}{3}} velocity of each mass is \frac{v}{2} = \sqrt{\frac{gh}{6}}$

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