What is the decrease in weight of a body of mass `600 kg` when it is taken in a mine of the depth `5000 m` ? [Radius of earth `= 6400` km, `g = 9.8 m//s^(2)`]

Explanation

Given that `m = 600` kg, `d = 5000 m`, `R = 6400` km `= 6.4 xx 10^(6) m`.
Weight of the body on the surface of the Earth `= 600 xx 9.8 = 5880 N`
At depth d, gravitational acceleration is
`g_(d) = g[1-d/R]`
`g_(d) = g[1-(5000)/(6.4 xx 10^(6))]`
`:. g_(d) = g[1-(5)/(6400)] = 9.8xx 0.999`
`:. g_(d) = 9.7902 m//s^(2)`
Weight of the body at depth
`d = mg_(d)`
`= 600 xx 9.7902`
`= 5874.1N`
`:.` Decrease in weight `= mg - mg_(d) = 5880 - 5874.1`
`:.` Decreases in weight `= 5.9 N`