Question

A body weighs 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 C $\frac{4W}{9}$

$\text{At the surface}$

$W=\frac{GMm}{R^2}......\left(I\right)$

$W^{\prime }=\frac{GMm}{(\frac{3R}{2}{)}^2}.......\left(II\right)$

$\frac{W}{W^{\prime }}=\frac{\frac{GMm}{R^2}}{\frac{GMm}{9R^2/4}}$

$\Rightarrow \frac{W}{W^{\prime }}=\frac{9}{4}$

$\Rightarrow W^{\prime }=\frac{4W}{9}$