A point mass m 0 is at the surface of a planet of density - and radius r- Gravitational force experienced by m 0 is proportional to 1A- r21B- r2C- rD- r 3

The correct option is C rWe know, gravitational force F=Gm_1m_2r^2 and density ρ=massvolume Let the mass of the planet be m then, nbsp; F=G m_o mr^2 = G m_or ...

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Standard XII

Physics

Newton's Law of Gravitation

A point mass ...

Question

A point mass $(m_{o})$ is at the surface of a planet of density $ρ$ and radius $r$ . Gravitational force experienced by $m_{o}$ is proportional to

\frac{1}{r^{2}}

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\frac{1}{r^{2}}

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r

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r^{3}

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Solution

The correct option is C $r$
We know, gravitational force $F = \frac{G m_{1} m_{2}}{r^{2}}$ and
density $ρ = \frac{m a s s}{v o l u m e}$
Let the mass of the planet be $m$ then,
$F = \frac{G m_{o} m}{r^{2}} = \frac{G m_{o}}{r^{2}} (ρ \frac{4 π r^{3}}{3})$
$= \frac{4 π ρ G m_{o}}{3} r$
$F \propto r$

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