Two equal masses each in are hung from a balance whose scale pans differ in vertical height by `h`. The error in weighing in terms of density of the earth `rho` is

Options

A. `piG rhomh`
B. `1/3 pi G rho mh`
C. `8/3 pi G rho mh`
D. `4/3 pi G rho mh`

Answer

C

Explanation

`g_(1) = g/([1 + h/R]^(2)) = g[1-(2h)/R]`
`W_(2) - W_(1) = mg_(2) - mg_(1)`
`=2mg [h_(1)/R - h_(2)/R] = 2m(GM)/R^(2). h/R`
`therefore g = (GM)/R^(2) " and " h_(1) - h_(2) = h`]
`therefore W_(2) - W_(1) =` error in weighing
`= 2mG.4/3piR^(3)rho h/R^(3) =(8pi)/3 Gm rhoh`