If change in value of ' g ' at a height ' h ' above surface of earth is same as at a

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7.Gravitation

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If the change in the value of ' $g$ ' at a height ' $h$ ' above the surface of the earth is same as at a depth $x$ below it, then ( $x$ and $h$ being much smaller than the radius of the earth)

A

$x=h$

B

$x=2 h$

C

$x=\frac{h}{2}$

D

$x=h^2$

Solution

(b)

$g_h=g\left(1-\frac{2 h}{R_e}\right)$

$g_x=g\left(1-\frac{x}{R_e}\right)$

According to the question,

$g_h-g=g_x-g$

$\Rightarrow g\left(-\frac{2 h}{R_e}\right)=g\left(\frac{-x}{R_e}\right)$

$\Rightarrow x=2 h$

Standard 11

Physics

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