A body has a weight of 90 kgf on the earth's | vedclass

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(D) The acceleration due to gravity on the surface of a planet is given by $g = \frac{GM}{R^2}$.Comparing the moon $(m)$ and the earth $(e)$:$\frac{g_

Vedclass · Accepted Answer

$40$

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(D) The acceleration due to gravity on the surface of a planet is given by $g = \frac{GM}{R^2}$.Comparing the moon $(m)$ and the earth $(e)$:$\frac{g_m}{g_e} = \frac{M_m}{M_e} 	imes \left( \frac{R_e}{R_m} ight)^2$.Given $M_m = \frac{1}{9} M_e$ and $R_m = \frac{1}{2} R_e$,we have:$\frac{g_m}{g_e} = \left( \frac{1}{9} ight) 	imes \left( \frac{R_e}{1/2 R_e} ight)^2 = \frac{1}{9} 	imes (2)^2 = \frac{4}{9}$.Therefore,$g_m = \frac{4}{9} g_e$.The weight of a body on the moon is $W_m = m \cdot g_m = m \cdot \left( \frac{4}{9} g_e ight) = \frac{4}{9} W_e$.Given $W_e = 90 \ kgf$,we get $W_m = \frac{4}{9} 	imes 90 = 40 \ kgf$.

$A$ body has a weight of $90 \ kgf$ on the earth's surface. The mass of the moon is $1/9$ of the earth's mass and its radius is $1/2$ of the earth's radius. On the moon,the weight of the body is .......... $kgf$.

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