Question

A body weighs $w$ 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. $\frac{9w}{27}$

Answer 1

The correct option is C $\frac{4w}{9}$

At the surface fo the earth, weight of the given mass $M$ is,

$w=Mg$

So, $M=\frac{w}{g}$

At height $(h=\frac{R}{2})$

$g^{\prime }=\frac{GM}{{(R+\frac{R}{2})}^2}=\frac{4}{9}\frac{GM}{R^2}\{\because g^{\prime }=\frac{GM}{(R+h{)}^2}\}$

Hence, $g^{\prime }=\frac{4}{9}g$

So, weight at $(h=\frac{R}{2})$

$w^{\prime }=M{g}^{\prime }$

$=\frac{w}{g}.\frac{4}{9}g$

$w^{\prime }=\frac{4}{9}w$

Why this question? The weight of an object varies with the height from the surface of a planet.