Question

A body weight W Newton at the surface of the earth. Its weight at a height equal to half the radius of the earth will be :

• A. $\frac{W}{2}$
• B. $\frac{2W}{3}$
• C. $\frac{4W}{9}$
• D. $\frac{W}{4}$

Answer 1

The correct option is A $\frac{W}{2}$

Given, $R=6400km,w=mg\Rightarrow g=\frac{w}{m}$

Now the weight of the body at the height is $\frac{1}{2}R$

$g^{\prime }=g(1-\frac{d}{R})$

So the weight of the body at the $\frac{1}{2}R$

$W^{\prime }=W(1-\frac{R}{2R})=W\frac{R}{2R})=\frac{W}{2}$