If both the mass and radius of earth decrease by `1%` the value of acceleration due to gravity will decrease by nearly:

Options

A. `1% `
B. `2%`
C. `1.5%`
D. `2.5%`

Answer

A

Explanation

`(g.)/(g)=(M.)/(M)xx((R )/(R.))^(2)=(0.99M)/(M)((R )/(.99R))^(2)=1.01`
`therefore (g.)/(g)-1=1.01-1 rArr (g.-g)/(g)=0.01`
or `(g.-g)/(g)xx100=1%`
So the correct choice is (a).