If both the mass and radius of the earth, each decreases by 50%, the acceleration due to gravity would

Options

A. increase by `50%`
B. decrease by `50%`
C. increase by `100%`
D. remain the same

Answer

C

Explanation

We have ,`g=(GM)/(R^(2))`
`g.(G((M)/(2)))/(((R)/(2)))=(2GM)/(R^(2))=2g`
`therefore%` increase in g `=(Deltag)/(g)xx100`
`=((g.-g)/(g))xx100`
`=((2g-g)/(g))xx100`
`=100%`