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.
Show Hint
Compare $g_h\approx g(1-\frac{2h}{R})$ and $g_d=g(1-\frac{d}{R})$.
Statement I is incorrect but statement II is correct
Both statement I and statement II are incorrect
Statement I is correct but statement II is incorrect
Both Statement I and II are correct.
Show Solution
The Correct Option isC
Solution and Explanation
Step 1: Think physically
Going down, only the mass inside the sphere of radius $r$ pulls, so $g$ drops linearly with depth. Going up, $g$ falls as the inverse square. Height reduces $g$ about twice as fast as depth for the same distance.
Step 2: Decide
So I holds and II does not. Option (C).
Final Answer:
Option (C).
\[ \boxed{\text{(C)}} \]