The distance through which one has to dig the | vedclass

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(A) The acceleration due to gravity at a depth $d$ below the surface of the earth is given by $g_d = g(1 - \frac{d}{R})$,where $g$ is the acceleration

Vedclass · Accepted Answer

$2560$

Vedclass · Answer

(A) The acceleration due to gravity at a depth $d$ below the surface of the earth is given by $g_d = g(1 - \frac{d}{R})$,where $g$ is the acceleration due to gravity at the surface and $R$ is the radius of the earth.Given that the acceleration due to gravity is reduced by $40 \%$,the value at depth $d$ becomes $g_d = g - 0.40g = 0.60g$.Substituting this into the formula: $0.60g = g(1 - \frac{d}{R})$.Dividing both sides by $g$: $0.60 = 1 - \frac{d}{R}$.Rearranging the terms: $\frac{d}{R} = 1 - 0.60 = 0.40$.Therefore,$d = 0.40 	imes R$.Given $R = 6400 \ km$,we have $d = 0.40 	imes 6400 \ km = 2560 \ km$.

The distance through which one has to dig the earth from its surface so as to reach the point where the acceleration due to gravity is reduced by $40 \%$ of that at the surface of the earth,is (radius of earth is $6400 \ km$) (in $km$)

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