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If a point mass m is on the axis of ring of mass M and radius R, then find time period of oscillations of SHM for small amplitude, ( g- acceleration due to gravity)

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$2 π \sqrt{\frac{R}{g}}$

$2 π \sqrt{\frac{R^{3}}{G M}}$

$2 π \sqrt{\frac{R^{3}}{2 G M}}$

$2 π \sqrt{\frac{2 R}{g}}$

answer is B.

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Detailed Solution

For small displacements , the gravitational field along the axis of ring is $E = - \frac{G M}{R^{3}} x$ ,

$F = - \frac{G M m}{R^{3}} x$

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