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. `piGrhomh`
B. `1/2piGrhomh`
C. `8/3piGrhomh`
D. `4/3piGrhomh`

Answer

C

Explanation

`g_(1)=g/([1+h/r]^(2))=g[1-(2h)R]`
`W_(2)-W_(1)=` error in weighing
`=2mg[(h_(1))/R-(h_(2))/R]=2m(Gm)/(R^(2))h/R`
`[:'g=(GM)/(R^(2))` and `h_(1)=h_(2)=h]`
Therefore `W_(2)-W_(1)=`error weighing
`=2mG4/3piR^(3)rhoh/(R^(3))=(8pi)/3Gmrhoh`