g at a depth d reduces to 25% from the value of surface of Earth. Calculate d if radius of Earth is 6400 km.

Dear student, 
let g is the acceleration due to gravity at the surface of the earth.
And g₁​​​​​​ be the acceleration due to gravity ata depth d from the surface of the earth,
so according to the problem 
g₁= (25g)/100 = 0.25g
​​​given radius of earth, r= 6400 km,
now the acceleration due to gravity at depth d related to acceleration due to gravity at earth surface is related by,
g₁=g(1-(d/r))
=) 0.25g = g(1-(d/r))
=) (d/r) = 1 - .25  = .75
=》d= .75×r = .75×6400 =4800km.

Regards.