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. w/2
• B. 2w/3
• C. 4w/9
• D. 9w/4

Answer 1

Answer: (C)

$\frac{4w}{9}$

Answer 2

The acceleration due to gravity at a height $h$ above Earth’s surface is given by:

$$g' = g\left(\frac{R}{R+h}\right)^2$$

For $h = \frac{R}{2}$,

$$g' = g\left(\frac{R}{R+\frac{R}{2}}\right)^2 = g\left(\frac{R}{\frac{3R}{2}}\right)^2 = g\left(\frac{2}{3}\right)^2 = \frac{4}{9}g$$

Since weight is proportional to the acceleration due to gravity, the weight at $h = \frac{R}{2}$ becomes:

$$w' = w \times \frac{4}{9} = \frac{4w}{9}$$