A man weighs `80 kg` on the surface of earth of radius `r`. At what height above the surface of earth his weight will be `40 kg`?

Options

A. 1000 km
B. 1500 km
C. 2650 km
D. 2900 km

Answer

C

Explanation

The weight of the man is reduced from 60 kg to 30 kg.
`therefore` At that height `g'=(g)/(2)`
But `(g')/(g)=(1)/(2)=(R^(2))/((R+h)^(2))=(1)/((1+(h)/(R ))^(2))`
`therefore 2 = (1+(h)/(R ))^(2) " " therefore 1 + (h)/(R )= sqrt(2)`
`therefore (h)/(R ) = sqrt(2) - 1 =1.414 - 1 = 0.414`
`therefore h = 0.414 R = 0.414xx 6400 = 2650 km`