A planet has a mass `M_(1)` and radius `R_(1).` The value of acceleration- due to gravity on its surface is `g_(1).` There is another planet 2, whose mass and radius both are two times that of the first planet. Which one of the following is the acceleration due to gravity on the surface of planet 2?

Options

A. `g_(1)`
B. `2g_(1)`
C. `g_(1)//2`
D. `g_(1)//4`

Answer

C

Explanation

The acceleration experienced by the mass `M_(1),` on planet
1 is given by
`g_(1)=GM_(1)//R_(1)^(2),`
Similarly the `g_(2)=G2M_(1)//4R_(1)^(2),`
hence, `g_(1)//g_(2)=2//1 or g_(2)=g_(1)//2`