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

Answer 1

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.