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 t

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.

TestHub · Accepted Answer

The acceleration due to gravity at a height $h$ above the earth's surface is given by $g_{h} = g (1 + \frac{h}{R})^{- 2}$ .

The acceleration due to gravity at a depth $d$ below the earth's surface is given by $g_{d} = g (1 - \frac{d}{R})$ .

From these expressions, it is clear that the value of $g$ decreases as we go above or below the earth's surface. Hence, Statement I is correct.

For $h = d$ , $g_{h}$ and $g_{d}$ are not equal. For example, if $h = d ≪ R$ , $g_{h} \approx g (1 - \frac{2 h}{R})$ and $g_{d} = g (1 - \frac{h}{R})$ , which are not equal. Hence, Statement II is incorrect.

Answer: Statement I is correct but statement II is incorrect

Physics - Gravitation Question with Solution | TestHub

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