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Question

# Suppose a planet exist whose mass and radius both are half of those of earth, calculate acceleration due to gravity on the surface of this planet. g = 9.8 m/s^2

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Solution

## As we know that the acceleration in earth is calculated by the formula (Gm)/(r^2) which equals 9.8m/s^2 where m is the mass of the earth and r is the radius of the earth. now, mass of that planet is half of earth so it's mass is (1/2)(m) and it's radius is half of earth so, it's radius is (1/2)(r) we will use the same formula to find the gravitational acceleration of that planet which equals { G (1/2)(m)}/ {(1/2)(r)}^2 = (Gm/2) ÷ (r^2 /4) = 4Gm / 2r^2 = 2Gm/ r^2 = (Gm/ r^2 ) × 2 now, substitute for Gm/r^2 of earth = 9.8 × 2 = 19.6m/s^2 so, the value of g on that planet will be 19.6m/s^2.

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