Question

a man weighs 90 newton on surface of the of the earth of radius R . at what height above the surface of earth his weight will be 40N.​

Answer 1

Given:

Weight of man on the surface of the earth= 90 N

Weight of man at the heigh H above the earth surface = 40 N

To find:

The height above the earth surface

Calculation:

The weight of the man at the surface of the earth is given by

    $W_{surface} = \frac{GMm}{R^2}$     ……(1)

The weight of the man at a height ‘H’ from the earth’s surface is given by

    $W_H=\frac{GMm}{(R+H)^2}$         ……(2)

By dividing equations (1) & (2)

    $\Rightarrow \frac{W_{surface}}{W_H} = \frac{\frac{GMm}{R^2}}{\frac{GMm}{(R+H)^2}} \\\\ \Rightarrow \frac{90}{40} = \frac{(R+H)^2}{R^2} \\\\\Rightarrow \frac{(R+H)}{R} = \frac{3}{2} \\\\\Rightarrow 2R+2H = 3R\\\\\Rightarrow R=2H\\\\ \Rightarrow H=\frac{R}{2}$

At a height of R/2 from the surface of the earth, weight will be 40 N

Answer 2

Answer:

I think ans should be (√2-1) R