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 depth ' \(d\) ' from earth's surface, if \(h = d\).
In the light of above statements, Choose the most appropriate answer form the options given below

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

Answer 1

The Correct Option is A

• Statement I: The acceleration due to gravity (g') decreases when moving away from the earth's surface either upwards or downwards. The formulae for variations are:

\[g' = g\left(1 - \frac{2h}{R}\right)\] (for height h above surface)

\[g' = g\left(1 - \frac{d}{R}\right)\] (for depth d below surface)

Both variations indicate a decrease in g.

• Statement II: At equal height h and depth d (h = d), the values of g' are not the same. This is because g decreases faster as we go up (due to the inverse square law) compared to going down (due to linear variation inside the earth).

Thus, Statement I is correct, and Statement II is incorrect.

Answer 2

The correct answer is (A) : Statement I is correct but statement II is incorrect
$g^{\prime }=\frac{g}{{\left(1+\frac{h}{R}\right)}^2}$
$g^{\prime }=g\left\{1-\frac{d}{R}\right\}$

Statement I is correct & Statement II is incorrect