Question

The radius of the earth is 6370 km and of mars is 3400 km. If an object of 200 N weighs on earth what will be the weight on mars? The mass of mars is 0.11 that of earth.

Answer 1

Let the mass of earth and the mass of the body are m₁ and m respectively.
Then the mass of mars is = 0.11 m₁.
Radius of earth = r₁ = 6370km
Radius of mars = r₂ = 3400km
Weight of the body on earth is W = 200N.
∴ $W_e$ = Gm₁m/(r₁)²..................(i)

The weight of the same object on the mars is given by
or, $W_m$ = G×0.11m₁m/(r₂²)................(ii)

Dividing equation (ii) by equation (i) we get,

$\frac{W_m}{W_e}=\frac{0.11r_1^2}{r_2^2}$
$W_m=\frac{0.11r_1^2}{r_2^2}\times W_e$
or, $W_m$ = (0.11×6370²×200)/(3400)²
or, $W_m$ = (0.11×6370×6370×200)/(3400×3400)
or, $W_m$ = (22×637×637)/(34×3400)
or, $W_m$ = 8926918/115600
or, $W_m$ = 77.22 N.