If the mass of earth is eighty times the mass of a planet and diameter of the planet is one fourth that of earth, then acceleration due to gravity on the planet would be

Options

A. 7.8 m/`s^(2)`
B. 9.8 m/`s^(2)`
C. 6.8 m/`s^(2)`
D. 2.0 m/`s^(2)`

Answer

D

Explanation

Since gravitational acceleration on earth is defined as
`g_(e) = (GM_(e))/(R_(e)^(2)) " "`.... (i)
mass of planet is `M_(p) = (M_(e))/(80) ` & radius `R_(p) = (R_(e))/(4)`
So `g_(p) = (GM_(P))/(R_(P)^(2)) " "`.... (ii)
From (i) & (ii), we get
`g_(P) = g_(e)" "(M_(p))/(R_(p)^(2)) xx (R_(e)^(2))/(M_(e)) = (g_(e))/(5) = 2 m//sec^(2) ("as g = 10m"//sec^(2))`