The radius of the Earth is about 6400 ; km an | vedclass

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(A) Given: Radius of Earth $R_e = 6400 \; km$,Radius of Mars $R_m = 3200 \; km$.Mass of Earth $M_e = 10 M_m$,Weight on Earth $W_e = 200 \; N$.The weig

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$80$

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(A) Given: Radius of Earth $R_e = 6400 \; km$,Radius of Mars $R_m = 3200 \; km$.Mass of Earth $M_e = 10 M_m$,Weight on Earth $W_e = 200 \; N$.The weight of an object is given by $W = mg$,where $g = \frac{GM}{R^2}$.Therefore,the ratio of weights is $\frac{W_m}{W_e} = \frac{m g_m}{m g_e} = \frac{M_m}{M_e} 	imes \left(\frac{R_e}{R_m}ight)^2$.Substituting the values: $\frac{W_m}{200} = \frac{1}{10} 	imes \left(\frac{6400}{3200}ight)^2$.$\frac{W_m}{200} = \frac{1}{10} 	imes (2)^2 = \frac{4}{10} = 0.4$.$W_m = 200 	imes 0.4 = 80 \; N$.

The radius of the Earth is about $6400 \; km$ and that of Mars is $3200 \; km$. The mass of the Earth is about $10$ times the mass of Mars. An object weighs $200 \; N$ on the surface of the Earth. Its weight on the surface of Mars will be .......... $N$.

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