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  4. The value of acceleration due to gravity 'g', at earth's surface is 10 m / s 2 . Its value at the centre of the earth which is assumed to be sphere of radius ' R' and uniform mass density, is

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Q. The value of acceleration due to gravity $'g'$, at earth's surface is $10\, m / s ^{2} .$ Its value at the centre of the earth which is assumed to be sphere of radius $' R'$ and uniform mass density, is

AIIMSAIIMS 1997Gravitation

Solution:

Acceleration due to gravity at a depth h from the earth’s surface
$\quad\quad g'=g\left(1-\frac{h}{R}\right)=g\left(1-\frac{R}{R}\right)=g\left(1-1\right)=0.$