QJEEM20Ph1b54: JEE Main 2020 Physics - Class 11 JEEM20Ph1b54 Solution: The value of the acceleration due to gravity is g 1 at a height …

Question

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The value of the acceleration due to gravity is g₁ at a height h =

{R \over 2}

(R = radius of the earth) from the surface of the earth. It is again equal to g₁ at a depth d below the surface of the earth. The ratio

\left( {{d \over R}} \right)

equals :

Accepted Answer

Given,

{g_{at\,high}} = {g_{at\,depth}}

We know,

{g_{depth}} =

g\left( {1 - {d \over R}} \right)

\therefore

g\left( {1 - {d \over R}} \right) = {{GM_e} \over {{{(R + h)}^2}}}

\Rightarrow

g\left( {1 - {d \over R}} \right) =

{{G{M_e}} \over {{{\left( {R + {R \over 2}} \right)}^2}}}

=

{4 \over 9}{{G{M_e}} \over {{R^2}}}

=

{4 \over 9}g

\Rightarrow

{d \over R} = 1 - {4 \over 9} = {5 \over 9}

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