If the earth suddenly shrinks (without changing mass) to half of its present radius, then acceleration due to gravity will be

Options

A. `(g)/(2)`
B. `(g)/(4)`
C. 2 g
D. 4 g

Answer

D

Explanation

`g=(GM)/(R^(2)),g'=(GM)/((R//2)^(2))=(4GM)/(R^(2))`
`therefore g'=4g`