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>>Physics
>>Gravitation
>>Variation in Value of Acceleration due to Gravity
>> $The change in the value of g at a height$

Question

The change in the value of $g$ at a height $h$ about the surface of the earth is the same as at a depth $d$ below the surface of earth. When both $d$ and $h$ are much smaller than the radius of earth, then which one of the following is correct?

A

$d = h$

B

$d = 2 h$

C

$d = \frac{3 h}{2}$

D

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

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Updated on : 2022-09-05

Solution

Verified by Toppr

Correct option is B)

Acceleration due to gravity at a height $h$ , $g_{h}^{'} = g (1 - \frac{2 h}{R})$
Acceleration due to gravity at a depth $d$ , $g_{d}^{'} = g (1 - \frac{d}{R})$
$∴ g (1 - \frac{2 h}{R})$ $= g (1 - \frac{d}{R})$
or $\frac{2 h}{R} = \frac{d}{R}$
or $d = 2 h$ .

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