Two planets A and B have the same mass M and | vedclass

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(C) The acceleration due to gravity $g$ at the surface of a planet is given by the formula:$g = \frac{GM}{R^2}$where $G$ is the universal gravitationa

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$1$

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(C) The acceleration due to gravity $g$ at the surface of a planet is given by the formula:$g = \frac{GM}{R^2}$where $G$ is the universal gravitational constant,$M$ is the mass of the planet,and $R$ is its radius.According to the problem,both planets $A$ and $B$ have the same mass $M$ and the same radius $R$.Since $g$ depends only on the mass $M$ and the radius $R$ of the planet,and both are identical for planets $A$ and $B$,the acceleration due to gravity at the surface of both planets must be equal.Therefore,the ratio of the acceleration due to gravity at the surface of planet $A$ to that of planet $B$ is:$\frac{g_A}{g_B} = \frac{GM/R^2}{GM/R^2} = 1$Thus,the correct option is $C$.

Two planets $A$ and $B$ have the same mass $M$ and radius $R$. The variation of density $\rho$ of the planets with distance $r$ from the center is shown in the following diagrams. The ratio of acceleration due to gravity at the surface of the planets $A$ and $B$ will be:

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