Question

Which one of the following describes the relation between the acceleration of a body in space and the distance (r) of the body from the center of the earth?

• A. 1/r
• B. 1/r³
• C. 1/r²
• D. r

Hint:

Gravity follows the "Inverse Square Law"—if you double the distance, the pull drops to one-fourth.

Answer 1

The Correct Option is C

Step 1: Concept
Newton's Law of Universal Gravitation states that the gravitational force is $F = G M m / r^2$.

Step 2: Meaning
Acceleration ($a$) is defined as Force divided by mass ($F/m$).

Step 3: Analysis
Dividing the gravitational force equation by the mass of the body ($m$), we get $a = GM/r^2$. Since $G$ and $M$ (mass of Earth) are constants, $a \propto 1/r^2$.

Step 4: Conclusion
The acceleration is inversely proportional to the square of the distance from the center of the Earth. Final Answer: (C)