Question

At a height 'R' above the earth's surface the gravitational acceleration is (R = radius of earth, g = acceleration due to gravity on earth's surface)

• A. $g$
• B. $\frac{g}{8}$
• C. $\frac{g}{4}$
• D. $\frac{g}{2}$

Hint:

Always remember that gravity follows an inverse-square law relative to the distance from the center of the planet. Doubling your distance from the center ($R \rightarrow 2R$) means the gravitational pull drops by a factor of $2^2 = 4$, yielding $\frac{g}{4}$ instantly!

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Find the acceleration due to gravity g' at a height h = R above the Earth's surface in terms of surface gravity g.

Step 2: Key Formula or Approach:
g' = g [R/(R+h)]². Substitute h = R.

Step 3: Detailed Explanation:
g' = g [R/(2R)]² = g (1/2)² = g/4.

Step 4: Final Answer:
g' = g/4, matching option (C).