Question

answer this question with clear explanation please explain​

Answer 1

Answer:

hey buddy !

option (a) is the correct ans.

hope it helps..

Answer 2

Answer:

To find:

Variation of gravitational acceleration with Depth d .

Solution:

Similar to Gauss' Theorem in Electrostatics , only the amount of mass enclosed at a depth d contributes to gravitational acceleration at that depth. Because of this reason , gravity at centre of Earth is zero.

At Earth surface , the gravitational acceleration be g.

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \red{ \bold{g = \dfrac{GM}{ {R}^{2} } }}}$

But at a depth , let the gravitational acceleration be g_{d}.

We shall try to get the mass enclosed by dividing the total mass of Earth with total volume and Multiplying it with an enclosed volume.

$g_{d} = \dfrac{G \bigg \{ \dfrac{M}{ \dfrac{4}{3} \pi {R}^{3} } \bigg \}\times \dfrac{4}{3} \pi {(R - d)}^{3} }{ {(R - d)}^{2} }$

Simplifying this we get :

$= > g_{d} = \dfrac{GM}{ {R}^{2} } \times (1 - \dfrac{d}{R} )$

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

So correct option : a)