A uniform sphere of mass M and radius R is su | vedclass

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(A) The gravitational force on the point mass $m$ due to the inner uniform sphere of mass $M$ is given by Newton's law of gravitation as $F_1 = \frac{

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$\frac{G M m}{x^2}$

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(A) The gravitational force on the point mass $m$ due to the inner uniform sphere of mass $M$ is given by Newton's law of gravitation as $F_1 = \frac{G M m}{x^2}$,acting towards the center.The gravitational force on the point mass $m$ due to the outer spherical shell of mass $M$ and radius $2R$ is zero. This is because,according to the shell theorem,the gravitational field inside a uniform spherical shell is zero everywhere,as the gravitational forces exerted by different parts of the shell on the point mass cancel each other out completely.Therefore,the net gravitational force on the particle is $F_{net} = F_1 + 0 = \frac{G M m}{x^2}$.

$A$ uniform sphere of mass $M$ and radius $R$ is surrounded by a concentric spherical shell of the same mass but radius $2R$. $A$ point mass $m$ is kept at a distance $x$ $(R < x < 2R)$ in the region bounded by the spheres as shown in the figure. The net gravitational force on the particle is:

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