Suppose mass and radius of the planet are half and twice that of earth's respectively. If acceleration due to gravity of the earth is 10m/S2. Find acceleration due to gravity of that period

The acceleration due to gravity of that planet is, gₐ = 1.25 m/s²

Explanation:

Given that,

Mass of the planet, m = 1/2M

Radius of the planet, r = 2R

Where M and R is the mass and radius of the Earth respectively.

The acceleration due to gravity of Earth, g = 10 m/s²

The acceleration due to gravity of Earth is given by the relation,

g = GM/R²

Similarly, the acceleration due to gravity of that planet is

gₐ = Gm/r²

where G is the Universal gravitational constant

On substituting the values in the above equation

gₐ = G (1/2 M) / 4 R²

= GM/8R²

= 1/8 (10 m/s²)

= 1.25 m/s²

Hence, the acceleration due to gravity of that planet is, gₐ = 1.25 m/s²