Question

A man weight $W$ on the surface of the earth and his weight at a height $R$ from surface of the earth is ($R$ is radius of the earth)

• A. $\frac{W}{4}$
• B. $\frac{W}{2}$
• C. $W$
• D. $4W$

Answer 1

The correct option is A $\frac{W}{4}$

R.E.F image

Since the weight of

man on the surface

of earth is 'w'

$\Rightarrow$ mass of man $\left(m\right)=\frac{w}{g}$

Applying Newton's low of

gravitation

$W=\frac{G{m}_{e}w/g}{R^2}$ (on surface of earth)

$\Rightarrow 1=\frac{G_{me}}{g{R}^2}$____(1)

Let us take,

at height 'R' from earth's surface,the weight

of man become ${}^{\prime }{w}_o^{\prime }$

$\Rightarrow W_o=\frac{G_{me}\left(w/g\right)}{(R+R{)}^2}$

$=W_o=\frac{G_{me}W}{4g{R}^2}$____(ii)

ending (i) & (ii)

$\frac{1}{W_o}=\frac{1}{w/4}$

$w_o=\frac{w}{4}$