The ratio of acceleration due to gravity at a depth (h) below the surface of earth and at a height above the surface of earth for h << $R_{e}$ ( radius of earth ):

Is constant

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Increase linearly with h

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Increase parabolically with h

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Decrease

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Solution

The correct option is B
Increase linearly with h

Let R be the radius of earth and g the acceleration due to gravity on earth’s surface. Then the desired ratio (say x) is:
$x = (1 - \frac{h}{R}) {(1 + \frac{h}{R})}^{2} = 1 + \frac{h}{R}$

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The ratio of acceleration due to gravity at a depth (h) below the surface of earth and at a height above the surface of earth for h << Re( radius of earth ):

The correct option is B Increase linearly with h Let R be the radius of earth and g the acceleration due to gravity on earth’s surface. Then the desired ratio (say x) is: x=(1−hR)(1+hR)2=1+hR

The ratio of acceleration due to gravity at a depth (h) below the surface of earth and at a height above the surface of earth for h << $R_{e}$ ( radius of earth ):

The correct option is B
Increase linearly with h

Let R be the radius of earth and g the acceleration due to gravity on earth’s surface. Then the desired ratio (say x) is:
$x = (1 - \frac{h}{R}) {(1 + \frac{h}{R})}^{2} = 1 + \frac{h}{R}$