Question

If the radius of the earth be increased by a factor of5 by what factor its density be changed to keep the value of g unchaned

Answer 1

Answer:

F = m g = G M m / R^2     gravitational force on mass m

g = G M / R^2      

M = p V = p * 4/3 pi R^3     where p is the density

g = G * p * 4/3 * pi ^ R^3 / R^2  = G p * 4/3 * pi * R    substituting for M

g2 / g1 = p2 R2 / (p1 R1) = 1 if g is to remain constant

p2 / p1 = R1 / R2 = 1/5   and p2 / p1 = 1/5