Question

Given below are two statements:
Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
Statement II: Acceleration due to earth's gravity is same at a height '\(h\)' and depths '\(d\)' from earth's surface, if \(h = d\).
In the light of above statements, choose the most appropriate answer from the options given below.

• A. Statement I is incorrect but statement II is correct
• B. Both statement I and statement II are incorrect
• C. Statement I is correct but statement II is incorrect
• D. Both Statement I and II are correct.

Hint:

Compare $g_h\approx g(1-\frac{2h}{R})$ and $g_d=g(1-\frac{d}{R})$.

Answer 1

The Correct Option is C

Step 1: Statement I
Above the surface, \(g\) falls as \(\frac{1}{r^2}\). Below the surface, \(g=g_0\frac{r}{R}\) falls linearly to zero at the centre. \(g\) is greatest at the surface. So statement I is correct.

Step 2: Statement II
For small \(h\): \(g_h=g\left(1-\frac{2h}{R}\right)\). For small \(d\): \(g_d=g\left(1-\frac{d}{R}\right)\).
Setting \(h=d\) gives different values. They are equal only when \(d=2h\). So statement II is incorrect.

Step 3: Result
Statement I is correct and II is incorrect. Option (C).

Final Answer:
Statement I is correct, II is incorrect, option (C). \[ \boxed{\text{(C)}} \]