An astronaut on a strange planet finds that acceleration due to gravity is twice as that on the surface of earth. Which of the following could explain thin ?

Options

A. Both the mass and radius of the planet are half as that of earth.
B. Radius of the planet is half as that of earth but the mass is the same as that of earth
C. Both the mass and radius of the planet are twice as that of earth.
D. Mass of the planet is half as that of earth but radius is same as that of earth.

Answer

A

Explanation

Acceleration due to gravity on the surface of the earth is
`g_(e)=(GM_(e))/(R_(e)^(2))`
where `M_(e)` and `R_(e)` are the m,ass and the radius of the earth respectively.
Acceleration due to gravity on the surface of the planet is
`g_(p)=(GM_(p))/(R_(p)^(2))`
where `M_(p)` and `R_(p)` be the mass and the radius of the planet respectively.
If both mass and radius of the planet are half as that of the earth, then
`g_(p)=(G(M_(e)//2))/((R_(e)//2)^(2))=2(GM_(e))/(R_(e))=2g_(e)`