A man weighs 50 kg at earth's surface. At what height above the earth's surface his weight becomes half (Radius of earth = 6400 km) :

Options

A. 2526 km
B. 6400 km
C. 2650 km
D. 3200 km.

Answer

C

Explanation

`(mg.)/(mg)=(1)/(2) rArr (g.)/(g)=(1)/(2)`
or `(R^(2))/((R+h)^(2))=(1)/(2) rArr (R )/(R+h)=(1)/(sqrt(2))`
`therefore sqrt(2)R=R+h`
`h=(sqrt(2)-1)R=0.414xx6400=2650` km.
Thus correct choice is (c ).