how far should a man go from the centre of the earth such that his wieght is 1/4th that on the earth?radius of the earth=6400km.

The weight of the man = mg.

Value of g = GM/(R*R), where G is gravitational constant

M is mass of earth and R is radius of the earth.

Hence, to be weight equal to 1/4

g' = g/4

This means

GM/(R'*R') = (1/4)GM/(R*R)

This means

R'=2*R

Hence the R' = 2* 6400

=    12800 km

Hence the man should go at a distance of 12800 km from the earth in order to reduce his weight to 1/4.

 

Regards,