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Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationField & ForceMedium2 minPYQ_2018

PhysicsMediumsingle choice

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the $n^{t h}$ power of R. If the period of rotation of the particle is T, then:

Options:

Answer:

Solution:

$F = \frac{K}{R^{n}}$ $\Rightarrow \frac{m V^{2}}{r} = \frac{K}{R^{n}}$ $\Rightarrow V^{2} \propto \frac{K}{R^{n - 1}}$
$\Rightarrow V \propto \frac{1}{R^{\frac{n - 1}{2}}}$ $\Rightarrow T = \frac{2 π R}{V} \propto \frac{R}{V}$
$\Rightarrow T \propto \frac{R}{\frac{1}{R^{\frac{n - 1}{2}}}}$ $\Rightarrow T \propto R^{\frac{n + 1}{2}}$

Stream:JEESubject:PhysicsTopic:GravitationSubtopic:Field & Force

⏱ 2mℹ️ Source: PYQ_2018

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