How much deep inside the earth (radius R ) should a man go, so that his weight becomes one-fourth of that on the earth's surface?

Step-by-step solution

Suppose depth inside the earth is h . As we know that, inside the earth g_i ( R-h R^3 ) ....(i) On the surface of the earth g_s 1 R^2 ....(ii) From Eqs. (i) and (ii), we get g_i g_c = (R-h) R^2 R^3 = R-h R 1 4 = R-h R R=4 R-4 h 3 R=4 h h= 3 4 R .