R and r are the radii of the Earth and Moon r | vedclass

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(A) The acceleration due to gravity $g$ on the surface of a spherical body of radius $R$ and density $\rho$ is given by the formula:$g = \frac{GM}{R^2

Vedclass · Accepted Answer

$\frac{R}{r} \cdot \frac{\rho_e}{\rho_m}$

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(A) The acceleration due to gravity $g$ on the surface of a spherical body of radius $R$ and density $ho$ is given by the formula:$g = \frac{GM}{R^2}$Since the mass $M = 	ext{Volume} 	imes 	ext{Density} = \frac{4}{3}\pi R^3 ho$,we substitute this into the formula:$g = \frac{G}{R^2} \left( \frac{4}{3}\pi R^3 ho ight) = \frac{4}{3}\pi G R ho$Thus,$g \propto Rho$.For the Earth and the Moon,the ratio of the accelerations due to gravity is:$\frac{g_e}{g_m} = \frac{R \cdot ho_e}{r \cdot ho_m} = \frac{R}{r} \cdot \frac{ho_e}{ho_m}$Therefore,the correct option is $A$.

$R$ and $r$ are the radii of the Earth and Moon respectively. $\rho_e$ and $\rho_m$ are the densities of the Earth and Moon respectively. The ratio of the accelerations due to gravity on the surfaces of the Earth and Moon is

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