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A point mass m is released from rest at a distance of 3R from the centre of a thin walled hollow sphere of radius R and mass M as shown. The hollow sphere is fixed in position and the only force on the point mass is the gravitational attraction of the hollow sphere. There is a very small hole in the hollow sphere through which the point mass falls as shown. The velocity of point mass when it passes through point P at a distance R/2 from centre of sphere, is

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$\sqrt{\frac{5 GM}{3 R}}$

$\sqrt{\frac{2 GM}{3 R}}$

$\sqrt{\frac{25 GM}{24 R}}$

None of these

answer is D.

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Detailed Solution

Inside spherical shell V is constant, so from energy conservation
$- \frac{GMm}{3 R} = \frac{{mv}^{2}}{2} - \frac{GMm}{R}$
Is $v = \sqrt{\frac{4 GM}{3 R}}$

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