If R is the radius of earth , the height ,at which the weight of a body becomes `1/4` of its weight on the surface of earth , is

Options

A. 2R
B. R
C. `R/2`
D. `R/4

Answer

B

Explanation

Acceleration due to gravity at hight h is, `g'=(g)/((1+(h)/R))^2`
`mg' = (mg)/((1+(h)/R)0^2`
`w'= (w)/((1+(h)/R))^2`
`Rightarrow (w)/4=(w)/((1+(h)/R))^2((therefore w' = w/4))`
`Rightarrow ((1+(h)/R))^2 = 4`
` Rightarrow 1+(h)/R =2`
`therefore h= R `