Question

If the mass of a planet is 10% less than that of the earth and the radius is 20% greater than that of the earth, the acceleration due to gravity on the plant will be

• A. 5/8 times on the surface of the earth
• B. 3/4 times that on the surface of the earth
• C. 1/2 times that on the surface of the earth
• D. 9/10 times that on the surface of the earth

Answer 1

The correct option is B 3/4 times that on the surface of the earth

Force due to gravity at earth's surface on a mass m:

F = GMm/R²

F = Gravitational Force

G = Gravitational Constant

M = Earth's Mass

m = mass of body

R = Earth's radius

The acceleration is F/m:

g = F/m = GM/R²

For a planet with 0.9M and 1.2R:

a = G(0.9M)/(1.2R)² = 0.625 (GM/R²) = 0.625g (62.5% of Earth's acceleration due to gravity)