The depth at which the effective value of acc | vedclass

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Question

(B) The acceleration due to gravity at a depth $d$ below the Earth's surface is given by the formula: $g' = g \left( 1 - \frac{d}{R} \right)$,where $g

Vedclass · Accepted Answer

$\frac{3R}{4}$

Vedclass · Answer

(B) The acceleration due to gravity at a depth $d$ below the Earth's surface is given by the formula: $g' = g \left( 1 - \frac{d}{R} \right)$,where $g$ is the acceleration due to gravity at the surface and $R$ is the radius of the Earth.Given that the effective value of acceleration due to gravity at depth $d$ is $g' = \frac{g}{4}$.Substituting this into the formula: $\frac{g}{4} = g \left( 1 - \frac{d}{R} \right)$.Dividing both sides by $g$: $\frac{1}{4} = 1 - \frac{d}{R}$.Rearranging the terms: $\frac{d}{R} = 1 - \frac{1}{4} = \frac{3}{4}$.Therefore,the depth is $d = \frac{3R}{4}$.

The depth at which the effective value of acceleration due to gravity is $\frac{g}{4}$ is

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