(C) Statement $I$ is correct: The acceleration due to gravity $g$ at a height $h$ above the surface is given by $g_h = g(1 + h/R)^{-2}$,which decrease

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Statement $I$ is correct but statement $II$ is incorrect

(C) Statement $I$ is correct: The acceleration due to gravity $g$ at a height $h$ above the surface is given by $g_h = g(1 + h/R)^{-2}$,which decreases as $h$ increases. At a depth $d$ below the surface,it is given by $g_d = g(1 - d/R)$,which decreases as $d$ increases.Statement $II$ is incorrect: For a height $h$ and depth $d$ where $h = d$,the values are $g_h = g(1 + h/R)^{-2}$ and $g_d = g(1 - h/R)$. Using binomial approximation for small $h$,$g_h \approx g(1 - 2h/R)$,while $g_d = g(1 - h/R)$. Since $(1 - 2h/R) \neq (1 - h/R)$,the values are not the same.

Class 11 Physics Gravitation Acceleration Due to Gravity and its Variation

Medium

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 from the options given below:

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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

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Gravitation

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Acceleration Due to Gravity and its Variation

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