Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighd 250 N on the surface ?

Options

A. 195 N
B. 240 N
C. 125 N
D. 210 N

Answer

C

Explanation

At a depth d below the surface of the earth,
`mg'=G(M'm)/(R-d)^(2)`
`M'=(4)/(3)pi(R-d)^(3)rho`
`implies g'=(Gm')/(R-d)^(2)`
`=4/3Gpi(R-d)rho`
If `d=-(R)/(2)` then
`g'=(4)/(3)Gpi rho=(2piRrho)/(3)`
On the surface of the earth
`g=(Gm)/(RV)=4/3 pi GRrho`
`therefore g'=(g)/(2)`
`therefore ` The body weighted 250 N on the surface of the earth would weight `1/2 xx 250` =125 N , half way down towards the centre of the earth.