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(B) For a particle moving in a circular orbit,the centripetal force is provided by the central attractive force.$F_c = \frac{k}{r^2} = m \omega^2 r$Re

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$r^{3/2}$

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(B) For a particle moving in a circular orbit,the centripetal force is provided by the central attractive force.$F_c = \frac{k}{r^2} = m \omega^2 r$Rearranging for angular velocity $\omega$:$\omega^2 = \frac{k}{mr^3}$$\omega = \sqrt{\frac{k}{m}} \cdot r^{-3/2}$The time period $T$ is given by $T = \frac{2\pi}{\omega}$.Substituting $\omega$:$T = \frac{2\pi}{\sqrt{\frac{k}{m}} \cdot r^{-3/2}} = 2\pi \sqrt{\frac{m}{k}} \cdot r^{3/2}$Thus,$T \propto r^{3/2}$.

$A$ particle moves in a circular orbit of radius $r$ under a central attractive force $F = -\frac{k}{r^2}$,where $k$ is a constant. The time period of its motion shall be proportional to

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