Mass remaining constant, the radius of the earth shrinks by 1%. The acceleration due to gravity on the earth's surface would

Options

A. decreases by `2%`
B. remain unchanged
C. increases by `2%`
D. increases by `1%`

Answer

C

Explanation

`(g')/(g)=(GM//R^(2)(1-1//100)^(2))/(GM//R^(2))=(1-1/100)^(-2)=1+2/100`
`((g')/g-1)xx100=2%`