A small point of mass $m$ is placed at a distance $2 R$ from the centre ' $O^{\prime}$ of a big uniform solid sphere of mass M and radius R. The gravitational force on ' m ' due to M is $\mathrm{F}_1$. A spherical part of radius $\mathrm{R} / 3$ is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be $\mathrm{F}_2$. The value of ratio $\mathrm{F}_1: \mathrm{F}_2$ is

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Aicharya · Accepted Answer

$\begin{aligned}
& \mathrm{F}_1=\frac{\mathrm{GMm}}{(2 \mathrm{R})^2}.....(1)\\ & \mathrm{~F}_2=\frac{\mathrm{GMm}}{(2 \mathrm{R})^2}-\left(\frac{\mathrm{G}\left(\frac{\mathrm{M}}{27}\right) \mathrm{m}}{\left(\frac{4 \mathrm{R}}{3}\right)^2}\right) \\ & \mathrm{F}_2=\frac{11}{48} \frac{\mathrm{GMm}}{\mathrm{R}^2}....(2)\\ & \mathrm{~F}_1: \mathrm{F}_2=12: 11
\end{aligned}$

A small point of mass $m$ is placed at a distance $2 R$ from the centre ' $O^{\prime}$ of a big uniform…

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