The magnitudes of the gravitational force at | vedclass

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(D) For a uniform sphere of mass $M$ and radius $R$,the gravitational field $g$ at a distance $r$ from the centre is given by:$1$. Inside the sphere $

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Both $(a)$ and $(b)$

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(D) For a uniform sphere of mass $M$ and radius $R$,the gravitational field $g$ at a distance $r$ from the centre is given by:$1$. Inside the sphere $(r $2$. Outside the sphere $(r > R)$: $g = \frac{GM}{r^2}$,which implies $g \propto \frac{1}{r^2}$.Since the gravitational force $F = mg$,the ratio of forces $\frac{F_1}{F_2}$ is equal to the ratio of gravitational fields $\frac{g_1}{g_2}$.If $r_1 If $r_1 > R$ and $r_2 > R$,then $\frac{F_1}{F_2} = \frac{r_2^2}{r_1^2}$. This matches option $(b)$.Therefore,both $(a)$ and $(b)$ are correct.

The magnitudes of the gravitational force at distances $r_1$ and $r_2$ from the centre of a uniform sphere of radius $R$ and mass $M$ are $F_1$ and $F_2$ respectively. Then

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