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

Options

A. `4.3 xx 10^(6)` m
B. `2.4 xx 10^(6)` m
C. `3.2 xx 10^(6)` m
D. `1.6 xx 10^(6)` m

Answer

A

Explanation

Given, `g=(1-(d)/(R))=(1)/(2)(g)/((1+(h)/(R))^(2))`
or `1-(d)/(R)=(1)/(2(1+(1600)/(6400))^(2))=(16)/(50)rArr(d)/(R)=(34)/(50)`
`:. d=(6.4xx10^(6)m)((34)/(50))=4.352 xx10^(6)m`