If the mass of a planet is `10%` less than that of the earth and the radius `20%` greater than that of earth, the acceleration due to gravity on the planet will be:

Options

A. `(1)/(2)` times that on the surface of the earth
B. `(3)/(4)` times that on the surface of the earth
C. `(5)/(8)` times that on the surface of the earth
D. `(9)/(10)` times that on the surface of the earth

Answer

C

Explanation

`g_(p)=(GM_(p))/(R_(p)^(2)) =(G[M-(10)/(100)M])/((R+(20)/(100)R)^(2))=(Gxx(9M)/(10))/((36R^(2))/(25))`
`g_(p)=(5)/(8)(GM)/(R^(2)) rArr g_(p)=(5)/(8)g`
So the correct choice is (c ).