Question

at what height will a man's height become half of his weight on surface of earth?​

Answer 1

Given:

• Man's weight becomes half as that of on the surface of earth .

To find:

• Height attained?

Calculation:

• Let height attained above earth surface be h and radius of earth be R .

• Let gravity at height be g_(h) and at surface be g_(s).

So, the weight at the height will be :

$w_{h} = \dfrac{ w_{s}}{2}$

$\implies m \times g_{h} = \dfrac{m \times g_{s}}{2}$

$\implies g_{h} = \dfrac{ g_{s}}{2}$

$\implies \dfrac{ g_{s}}{ {(1 + \frac{h}{R} )}^{2} } = \dfrac{ g_{s}}{2}$

$\implies \dfrac{ 1}{ {(1 + \frac{h}{R} )}^{2} } = \dfrac{ 1}{2}$

$\implies {(1 + \dfrac{h}{R} )}^{2} = 2$

$\implies 1 + \dfrac{h}{R} = \sqrt{2}$

$\implies \dfrac{h}{R} = \sqrt{2} - 1$

$\implies h = (\sqrt{2} - 1)R$

So, at (√2-1)R height, the weight will become half.