Question

A body weighs 45 N on the surface of the earth. The gravitational force on a body due to earth at a height equal to half the radius of earth will be ______.

• A. 20 N
• B. 22.5 N
• C. 30 N
• D. 36 N

Hint:

Never use the approximation $g' = g(1 - 2h/R)$ unless $h \ll R$ (less than 5% of the radius). For large heights like $h = R/2$, you MUST use the exact formula $g' = g [R / (R+h)]^2$ to get the correct answer!

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Weight is $mg$. Acceleration due to gravity at height $h$ is $g_h = g \left( \frac{R}{R+h} \right)^2$.

Step 2: Formula Application:
$h = R/2 \implies R+h = 1.5R = \frac{3}{2}R$.
$W_h = W \left( \frac{R}{3R/2} \right)^2$.

Step 3: Explanation:
$W_h = 45 \times \left( \frac{2}{3} \right)^2 = 45 \times \frac{4}{9} = 5 \times 4 = 20$ N.

Step 4: Final Answer:
The force at that height will be 20 N.