The depth at which acceleration due to gravity becomes n g is ( R = radius of earth, g = acceleration due to gravity) ( n = integer)

Question

The depth at which acceleration due to gravity becomes n g ​ is ( R = radius of earth, g = acceleration due to gravity) ( n = integer)

TestHub · Accepted Answer

The acceleration due to gravity at a depth $d$ is given by the formula:

$g_{d} = g (1 - \frac{d}{R})$

Given that $g_{d} = \frac{g}{n}$ , substituting this into the formula gives:

$\frac{g}{n} = g (1 - \frac{d}{R})$

Dividing both sides by $g$ :

$\frac{1}{n} = 1 - \frac{d}{R}$

Rearranging the terms to solve for $d$ :

$\frac{d}{R} = 1 - \frac{1}{n}$

$\frac{d}{R} = \frac{n - 1}{n}$

$d = \frac{R ( n - 1 )}{n}$

Answer: $\frac{R ( n - 1 )}{n}$

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