At what depth below the surface of the earth, acceleration due to gravity g will be half its value 1600km above the surface of the earth

Options

A. `4.2xx10^6m`
B. `3.19xx10^6m`
C. `1.59xx10^6m`
D. None of these

Answer

A

Explanation

According to question `(g_h)/2=g_d`
`g_h=g/((1+h/R)^2)=g/((1+1600/6400)^2)=16/25g`
`g_d=g(1-d/R)`
On putting value of `g_h` and `g_d` in eq. (i)
`16/50g=g(1-d/R)`
`rArrd=Rxx34/50=4.3xx10^6m`