Find the percentage decreases in weight of a body, when taken 16 km below the surface of the earth. Take radius of the earth as 6400 km.

Explanation

Here , R =6400km, x=16 km.
The value of acceleration due to gravity at a depth x,
`g^.=g(1-x/R)=g(1-(16)/(6400))`
`therefore g-g^.=1/(400)g=2.5xx10^(-3)g`
If m is the mass of the body, then mg and `mg^.` are the weight of the body on the surface of earth and at a depth of 16 km below the surface of the earth respectively . Then ,percentage decrease in the weight of the body
`=(mg-mg^.)/(mg)xx100`
`=(g-g^.)/(g)xx100=(2.5xx10^(-3))/(g)gxx100=0.25%`