Q128 / 150 · MHT CET 2026 (11 April Shift 1) · Physics
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.
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.
- AStatement I is incorrect but statement II is correct
- BBoth statement I and statement II are incorrect
- Correct answerCStatement I is correct but statement II is incorrect
- DBoth Statement I and II are correct.
Solution
The acceleration due to gravity at a height $h$ above the earth's surface is given by $g_h = g \left(1 + \dfrac{h}{R}\right)^{-2}$.
The acceleration due to gravity at a depth $d$ below the earth's surface is given by $g_d = g \left(1 - \dfrac{d}{R}\right)$.
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 $h = d \ll R$, $g_h \approx g \left(1 - \dfrac{2h}{R}\right)$ and $g_d = g \left(1 - \dfrac{h}{R}\right)$, which are not equal. Hence, Statement II is incorrect.
Answer: Statement I is correct but statement II is incorrect
The acceleration due to gravity at a depth $d$ below the earth's surface is given by $g_d = g \left(1 - \dfrac{d}{R}\right)$.
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 $h = d \ll R$, $g_h \approx g \left(1 - \dfrac{2h}{R}\right)$ and $g_d = g \left(1 - \dfrac{h}{R}\right)$, which are not equal. Hence, Statement II is incorrect.
Answer: Statement I is correct but statement II is incorrect
Hence, the correct answer is option: 'C'.