A body weighs W newton at the surface of the earth. Its weight at a height equal to half the radius of the earth, will be

Options

A. `(W)/(2)`
B. `(2W)/(3)`
C. `(4W)/(9)`
D. `(8W)/(27)`

Answer

C

Explanation

The value of acceleration due to gravity at a height h above the earth sruface is given by `g=(g)/(1+(h)/(R ))^(2)`
where R is radius of earth
when `h=(R )/(2) g' =(g)/(1+(1)/(2))^(2)=(4g)/(9)`
hence weight `w=mg=4/9 mg -4/9 w`