Question

What would be the accelearation due to gravity at a depth of 200 km from ythe earth surface assuming that earth has uniform denisty [Take ,R =6400 km]
A. 4.37 `ms^(-2)`
B. 6.737 `ms^(-2)`
C. 5.709 `ms^(-2)`
D. 4.751 `ms^(-2)`

Answer 1

Given depth d= 2000km =`=2x10^(6)m`
Radius of earth R=6400 km `=6.4xx10^(6)`m
The acceleration due to gravity at a point at a depth d from the earth surface is given by
`g_(d)=g[1-(d)/(R )]`
`therefore g_(d)=9.8[(1-(2xx10^(6))/(6.4xx10^(6)))]`
`=(9.8xx4.4)/(6.4)=6.737 ms^(-2)`