If the radius of the earth decreases by `10%`, the mass remaining unchanged, what will happen to the acceleration due to gravity?

Options

A. Decreases by `19%`
B. Increases by `19%`
C. Decreases more than `19%`
D. Increases more than `19%`

Answer

D

Explanation

`g=(GM)/(R^(2)).......(i)`
`g'=(GM)/((90/100R)^(2))=100/81 (GM)/(R^(2)).........(ii)`
From (i) and (ii), `g'=100/81g (g')/g=100/81`
`(g')/g-1=100/81-1`
`Deltag=19/81g=23%` of `g`
So increases is more than `19%` of `g`.