A body weighs 700 , gm , wt on the surface of | vedclass

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(B) The acceleration due to gravity on the surface of a planet is given by $g = \frac{GM}{R^2}$,where $G$ is the gravitational constant,$M$ is the mas

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$400$

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(B) The acceleration due to gravity on the surface of a planet is given by $g = \frac{GM}{R^2}$,where $G$ is the gravitational constant,$M$ is the mass of the planet,and $R$ is its radius.For Earth,$g_e = \frac{GM_e}{R_e^2}$.For the given planet,the mass $M_p = \frac{M_e}{7}$ and the radius $R_p = \frac{R_e}{2}$.Substituting these values,the acceleration due to gravity on the planet is $g_p = \frac{G(M_e/7)}{(R_e/2)^2} = \frac{GM_e/7}{R_e^2/4} = \frac{4}{7} \left( \frac{GM_e}{R_e^2} ight) = \frac{4}{7} g_e$.The weight of a body is given by $W = mg$. Since the mass $m$ of the body remains constant,the weight on the planet $W_p$ is related to the weight on Earth $W_e$ by $W_p = m g_p = m \left( \frac{4}{7} g_e ight) = \frac{4}{7} W_e$.Given $W_e = 700 \, gm \, wt$,we have $W_p = \frac{4}{7} 	imes 700 = 400 \, gm \, wt$.

$A$ body weighs $700 \, gm \, wt$ on the surface of the earth. How much will it weigh on the surface of a planet whose mass is $\frac{1}{7}$ and radius is half that of the earth?

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