If change in value of ‘g’ at a height h above surface of earth is same as at a depth x b

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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 the same as at a depth $x$ below it, then (both $x$ and $h$ being much smaller than the radius of the earth)

A

$x = h$

B

$x = 2h$

C

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

D

$x = {h^2}$

(AIEEE-2005)

Solution

(b) The value of $g$ at the height $h$ from the surface of earth $g' = g\,\left( {1 – \frac{{2h}}{R}} \right)$

The value of $g$ at depth $x$ below the surface of earth $g' = g\,\left( {1 – \frac{x}{R}} \right)$

These two are given equal, hence $\left( {1 – \frac{{2h}}{R}} \right) = \left( {1 – \frac{x}{R}} \right)$

On solving, we get $x = 2h$

Standard 11

Physics

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