Question

Assuming that Mars is a sphere of radius 3400 km and density 3900 kg m^-3 and that the Earth is a sphere 3 of radius 6370 km and density 5500 kg m^-3, calculate the value of acceleration due to gravity on the surface of Mars.
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Answer 1

Solution

Let the mass of earth and the mass of the body are m₁ and m respectively. Also let, g' is the gravitational acceleration on the mars.

Then the mass of mars is =0.11m₁.

Radius of earth=r₁=6370km

Radius of mars=r₂=3400km

Weight of the body on earth is 200N.

∴, mg'=Gm₁m/(r₂)²

or, mg'=G×0.11m₁m/(3400)²×(r₁²/r₁²)

or, mg'={(0.11×r₁²)/3400²}×(Gm₁m/r₁²)

or, mg'=(0.11×6370²×200)/(3400)²

or, mg'=(0.11×6370×6370×200)/(3400×3400)

or, mg'=(22×637×637)/(34×3400)

or, mg'=8926918/115600

or, mg'=77.22N

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