Question

How much deep inside earth ( radius r ) should a man go , so that his weight becomes 1/4 of that one the earth surface?

Answer 1

For the weight to become one-forth, this also means, that the effective acceleration due to gravity should become one - fourth.

Thus by the formula for effective g when we go under the surface

New g = g at surface { 1- d/R} where d is the depth under the surface

So,
g/4 = g ( 1-h/R)
1/4 = 1 - h/R
h/R = 3/4

So,
h = 3R/4
So, if the person goes 3R/4 under the surface of the earth , then the weight of the person will become one fourth that of the weight at the surface of earth.

R here, is radius of earth.

Answer 2

Answer:

g at surface or a depth is g×(1-h/r)