The mass of a planet is frac{1}{9} of the mas | vedclass

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(C) The acceleration due to gravity on the Earth is $g = \frac{GM_e}{R_e^2}$.Given,the mass of the planet $M_p = \frac{1}{9} M_e$ and the radius of th

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(C) The acceleration due to gravity on the Earth is $g = \frac{GM_e}{R_e^2}$.Given,the mass of the planet $M_p = \frac{1}{9} M_e$ and the radius of the planet $R_p = \frac{1}{2} R_e$.The acceleration due to gravity on the planet is $g_p = \frac{GM_p}{R_p^2}$.Substituting the values,$g_p = \frac{G(M_e/9)}{(R_e/2)^2} = \frac{G M_e / 9}{R_e^2 / 4} = \frac{4}{9} \frac{GM_e}{R_e^2} = \frac{4}{9} g$.The weight of the body on the Earth is $W_e = mg = 9 \ N$.The weight of the body on the planet is $W_p = mg_p = m(\frac{4}{9} g) = \frac{4}{9} (mg) = \frac{4}{9} 	imes 9 \ N = 4 \ N$.

The mass of a planet is $\frac{1}{9}$ of the mass of the Earth and its radius is half that of the Earth. If a body weighs $9 \ N$ on the Earth,its weight on the planet would be ........ $N$.

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