A body weighs 48 N on the surface of the earth. The gravitational force experienced by the body due to the earth at a height equa…

Question

A body weighs 48 N on the surface of the earth. The gravitational force experienced by the body due to the earth at a height equal to one-third the radius of the earth from its surface is:

1. A. 16 N
2. B. 27 N (Correct answer)
3. C. 32 N
4. D. 36 N

Correct Answer

Option B — 27 N

Detailed Solution & Explanation

The correct answer is 27 N.

Key Points

• At height $h$, $g_h=\dfrac{GM}{(R+h)^2}$, so $\dfrac{W_h}{W}=\dfrac{R^2}{(R+h)^2}$.
• With $h=\dfrac{R}{3}$: $\dfrac{W_h}{W}=\dfrac{R^2}{\left(\frac{4R}{3}\right)^2}=\dfrac{9}{16}$.
• $W_h=\dfrac{9}{16}\times 48=27$ N.