The value of acceleration due to gravity at a depth of 1600 km is equal to [Radius of earth = 6400 km]

Options

A. `9.8 ms^(-2)`
B. `4.9 ms^(-2)`
C. `19.6 ms^(-2)`
D. `7.35 m^(-2)`

Answer

D

Explanation

Given,
Depth (d) = 1600 km
We know that,
`g_(d)=g(1-(d)/(R ))`
Here, `g=9.8m//s^(2)`
R = 6400 km
`g_(d)=g(1-(1600)/(6400))`
`= 9.8 (1-(1)/(4))`
`=9.8((4-1)/(4))=(9.8xx3)/(4)`
`g_(d)=7.35 ms^(-2)`