A body weighs `700gm` wt on the surface of the earth. How much will it weigh on the surface of a planet whose mass is `1/7` and radius is half that of the earth

Options

A. `400 gm`
B. `300 gm`
C. `700 gm`
D. `500 gm`

Answer

A

Explanation

Let `M` and `R` be mass and radius of earth and `M`' and R' be mass and radius of the planet, then
`M' = (M)/(7)` and `R' = (R )/(2)`
On earth, `g = (GM)/(R^(2))`,
On planet, `g' = (GM')/(R^(2)) = (GM//7)/((R//2)^(2))`
`g' = (4)/(7) ((GM)/(R^(2))) = (4)/(7)g`
`:.` weight of body on planet `= mg'`
`= 700 xx (4)/(7) xx g = 400 gm wt`