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: Understanding the Concept
Acceleration due to gravity is largest at the surface of the earth. It falls both going up and going down.

Step 2: Statement (A)
At height \(h\): \(g_h=g\left(1-\frac{2h}{R}\right)\) approximately. At depth \(d\): \(g_d=g\left(1-\frac{d}{R}\right)\). Both are less than \(g\). So (A) is true.

Step 3: Statement (B)
For equal values, \(2h=d\), not \(h=d\). So the claim \(h=d\) is wrong.

Step 4: Statement (C)
At \(h=640\) km, \(g'=g\left(\frac{R}{R+h}\right)^2=g\left(\frac{1}{1.1}\right)^2\approx0.83g\). That is a decrease of about 17%, not 10%.

Step 5: Statement (D)
Rotation reduces the effective g at the equator, and at the poles there is no such reduction. The statement is the wrong way round.

Step 6: Conclusion
Only (A) is correct.

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