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A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0 , a force F = kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is:

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$2 \sqrt{\frac{k}{p}}$

$2 \sqrt{\frac{p}{k}}$

$\sqrt{\frac{2 p}{k}}$

$\sqrt{\frac{2 k}{p}}$

answer is B.

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Detailed Solution

$F = k t = \frac{d p}{d t} \int_{P}^{3 P} d p = \int_{0}^{T} k t d t 2 P = \frac{k T^{2}}{2} T = 2 \sqrt{\frac{p}{k}}$

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