The radius of the earth is about $$6400$$ km and that of mars is about $$3200$$ km. The mass of the earth is about $$10$$ times the mass of mars. An object weighs $$80$$ N on the surface of earth. What will be its weight (in$$ $$N) on the surface of mars?

Question

Infinity Learn · Accepted Answer

Let M and M be masses and R and R' be the radii of the earth and the mars respectively. If g and g' are the values of acceleration due to gravity on the surface of the earth and the mars respectively, then

$\begin{array}{l} \frac{g^{'}}{g} = \frac{{GM}^{'}}{R^{' 2}} \times \frac{R^{2}}{GM} = \frac{M^{'} R^{2}}{{MR}^{' 2}} \\ or g^{'} = \frac{M^{'} R^{2}}{{MR}^{' 2}} \times g \end{array}$

If m is mass of the body, then its weight on the mars,

${mg}^{'} = \frac{M^{'} R^{2}}{{MR}^{' 2}} \times mg$

$Here, M = 10 M, R = 6400 km, R^{'} = 3200 km and mg = 80 N$

$\Rightarrow {mg}^{'} = \frac{M^{'} \times (6400)^{2}}{10 M^{'} \times (3200)^{2}} \times 80 = 32 N$

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The radius of the earth is about 6400 km and that of mars is about 3200 km. The mass of the earth is about 10 times the mass of mars. An object weighs 80 N on the surface of earth. What will be its weight (in N) on the surface of mars?

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