Keeping the mass fixed , if the radius of the earth is halved, the acceleration due to gravity at any place will be

Options

A. half of the original
B. one-fourth of the original
C. doubled of the original
D. four times of the original

Answer

D

Explanation

Acceleration due to gravity,
`g=(GM)/(R^2)`
Keeping the mass fixed , if the radius of the earth is halved, the acceleration due to gravity becomes,
`g^.=(GM)/(R/2)^2=(4GM)/(R^2)=4g or, (g^.)/g=4`