The correct option is C
(√2−1)R
Weight of the man on the surface of the earth, W = 80 N
Weight of the man at height h from the surface of the earth, Wh=40N
Weight of the man of mass m at the surface of the earth, W=mg=mGMR2
Here, M = Mass of the earth, R = Radius of the earth and G = Gravitational constant
Weight of the man at height h from the surface of the earth, Wh=mgh=mGm(R+h)2
Taking ratio of Wh and W:WhW=(RR+h)2⇒(RR+h)2=4080=12⇒RR+h=1√2⇒√2R=R+h⇒h=√2R−R⇒h=(√2−1)R
Thus, at height (√2−1)R, the man weighs 40 N.
Hence, the correct answer is option (c).