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Does the value of g change while going d...

Does the value of g change while going deep inside the earth ? Why ?

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(i) The acceleration due to gravity (g) on earth's surface is given as , `g=(GM)/(R^2)`
The value of g depends on the mass M of the earth and the radius R of the earth .
(ii) As we go inside the earth decreses and no longer remains equal to the radius of the earth (R).
(iii) Along with the distance , the part of the earth which contributes towards the gravitational force felt also decreases, decreasing the value of (M).
(iv) Due to to combined result of change in R and M, value of g decreases - as we go inside the earth and becomes zero at the centre of the earth .
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Knowledge Check

  • The Earth is not a perfect sphere. Due to the flattening of Earth at the poles, the radius of Earth is minimum at the poles and hence the value of g is maximum at the poles. One the other hand, the radius of the Earth is maximum at the equator of the Earth. As the mass and radius of moon are smaller than that of the Earth, so the value of g on moon is 1 . 63 m//s ^(2) . As we go up from the surface of the Earth, the distance from the centre of the Earth increases and hence the value of g decreases. The value of g decreases as we go down inside the Earth and it become zero at the centre of the Earth . What will be the unit of (G)/( g) ?

    A
    `m^(2) kg^(2)`
    B
    `m^(-1) kg^(2)`
    C
    `m^(2) kg^(-1)`
    D
    ` m^(-2) kg`

  • The Earth is not a perfect sphere. Due to the flattening of Earth at the poles, the radius of Earth is minimum at the poles and hence the value of g is maximum at the poles. One the other hand, the radius of the Earth is maximum at the equator of the Earth. As the mass and radius of moon are smaller than that of the Earth, so the value of g on moon is 1 . 63 m//s ^(2) . As we go up from the surface of the Earth, the distance from the centre of the Earth increases and hence the value of g decreases. The value of g decreases as we go down inside the Earth and it become zero at the centre of the Earth . What is the value of acceleration due to gravity on the surface of Earth ?

    A
    `10 . 5 m^(2) s^(-1)`
    B
    `9 . 8 m s^(-2)`
    C
    ` 9 . 8 m^(2) s^(-1)`
    D
    ` 2 . 5 m s^(-1)`

  • The Earth is not a perfect sphere. Due to the flattening of Earth at the poles, the radius of Earth is minimum at the poles and hence the value of g is maximum at the poles. One the other hand, the radius of the Earth is maximum at the equator of the Earth. As the mass and radius of moon are smaller than that of the Earth, so the value of g on moon is 1 . 63 m//s ^(2) . As we go up from the surface of the Earth, the distance from the centre of the Earth increases and hence the value of g decreases. The value of g decreases as we go down inside the Earth and it become zero at the centre of the Earth . If the radius of the Earth were to shrink by 1% and its mass remaining the same, the acceleration due to gravity on the Earth's surface would

    A
    decreases
    B
    increases
    C
    remain unchanged
    D
    will decrease by ` 9 . 8 % `

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