Question

The weight of a body at a height of 3$R_E$ from the surface of the earth is 90 N, where $R_E$ is the radius of the earth. The weight of the same body at a height of $R_E$ from the surface of the earth is:

• A. 22.5 N
• B. 180 N
• C. 360 N
• D. 90 N

Hint:

Gravitational force decreases inversely with the square of distance from Earth's center. Always use total distance $(R_E + h)$, not just height $h$. Weight at surface is maximum and decreases with altitude. Ratios simplify calculations instead of using $G$, $M$, and $R$ explicitly.

Answer 1

The Correct Option is C

• Weight at height $h$ above the surface: \[ W_h = W_0 \left(\frac{R_E}{R_E + h}\right)^2 \] • For $h = 3R_E$, $W_{3R_E} = W_0 \left(\frac{R_E}{4R_E}\right)^2 = \frac{W_0}{16} = 90$ N.
\[ W_0 = 90 \times 16 = 1440 \text{ N} \] • For $h = R_E$, \[ W_{R_E} = 1440 \left(\frac{R_E}{2R_E}\right)^2 = 1440 \times \frac{1}{4} = 360 \text{ N} \] • Hence, the weight at height $R_E$ is 360 N.