Question

Select the correct statement out of the following

• A. Acceleration due to gravity decreases as we go up or down from earth's surface.
• B. Acceleration due to gravity is same at a height 'h' and depth 'd' from earth's surface, if \(h = d\).
• C. Acceleration due to gravity at 640 km above the earth surface decreases by 10% of its value at earth's surface (earth's radius is 6400 km)
• D. There is reduction in acceleration due to gravity at poles due to rotation of earth as the poles are lying on the axis of rotation and do not revolve.

Hint:

The value of g falls both above the surface and below it.

Answer 1

The Correct Option is A

Step 1: Approach
Check each statement with the formulas.

Step 2: Numbers
At 640 km, $R/(R+h)=1/1.1=0.909$, and squaring gives $0.826$. So $g$ drops by $17.4\%$.
Equal values of $g$ at height and depth need $\dfrac{2h}{R}=\dfrac dR$, so $d=2h$.
At the poles the centrifugal term $\omega^2R\cos^2\lambda$ is zero, so there is no reduction there.

Step 3: Conclusion
Statements B, C and D do not hold, and A does: $g$ decreases both up and down. Option (A).

Final Answer:
Gravity is greatest at the surface and falls above and below it, option (A). \[ \boxed{\text{(A)}} \]