Statement-1 : If body the mass and raiuds of the earth decrease by `1%`, the value of acceleration due to gravity will increase by `2%`.
Statement-2 : `g = GM//R^(2)`.

Options

A. Statement -1 is true , Statement -2 is true , Statement-2 is a correct explanation of Statement -1.
B. Statement -1 is true , Statement-2 is true , Statement-2 is a correct explanation of Statement-1.
C. Statement-1 is true , Statement-2 is false.
D. Statement-1 is false , Statement-2 is true.

Answer

D

Explanation

Here, statement-1 is wrong but statement-2 is correct.
Given `dm//m = - 1//100`
and `dR//R = - 1//100`
As `g = GM//R^(2)`
Taking log of both the sides and differtiating we get
`(dg)/(g) = (d M)/(M) - (2dR)/(R )`
`:. %` change in `g = (dg)/(g) xx 100`
`= [-(1)/(100) -2 ((-1)/(100))] xx 100 = 1%`
Positive sign shown that there is increase in the value of `g` by `1%`.