Question

An astronomical object has its mass 4 times the mass of earth and radius half of the radius of earth. If acceleration due to gravity at earth is g, find its value at the surface of the astronomical object.

Answer 1

Let x be the astronomical object

mass of x (M) = 4 times of mass of earth
= 4 × 5.972 × 10 ^ 24 kg
= 23.888 × 10 ^ 24 kg

radius of x (r)= 1/2 of radius of earth
= 1/2 × 6371 km
= 3185.5 km
= 3185500 m

we know that acceleration due to gravity on x = GM/r^2

= (6.673 × 10^-11 Nm^2kg^-2× 23.888 × 10^24 kg)/(31855)m^2

= 39.27224 ms^-2
therefore acceleration due to gravity on the astronomical object = 39.27224 ms^-2