A stone weighs 100N on the surface of the Earth. The ratio of its weight at a height of half the radius of the Earth to a depth of half the radius of the earth will be approximately

Options

A. 3.6
B. 2.2
C. 1.8
D. 0.9

Answer

D

Explanation

`(W_(h))/(W)=(mg.)/(mg)=(g.)/(g)`
`=(R^(2))/(((3R)/(2))^(2))=(4)/(9) rArr W_(h)=100xx(4)/(9)`
`(W_(d))/(W)=(g.)/(g)=1-(d)/(R )=1-(1)/(2)=(1)/(2) rArr W_(d)=100xx(1)/(2)`
`therefore (W_(h))/(W_(d))=((100xx4)/(9))/(100//2)=(8)/(9)=0.9`
So correct choice is (d).