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

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