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The earth is an approximate sphere. If t...

The earth is an approximate sphere. If the interior contained matter which is not of the same density every where, then on the surface of the earth, the acceleration due to gravity

A

Will be directed towards the centre but not the same everywhere.

B

Will have the same value everywhere but not directed towards the centre.

C

Will be same everywhere in magnitude directed towards the centre.

D

cannot be zero at any point.

Text Solution

Verified by Experts

The correct Answer is:
D
If the earth is an appoximate sphere of non-uniform density, then the centre of gravity of earth will not be situated at the centre of earth. The distance of different points on earth will be at different distances from the centre of gravity of earth. As, `g = (GM)/(r^(2))` or `g prop (1)/(r^(2))`, so is different on different points on the surface of earth but naver zero.
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Knowledge Check

  • The earth is an approximate sphere. If the interior contained matter which is not of the same density everywhere, then on the surface of the earth, the acceleration due to gravity.

    A
    will be directed towards the centre but not the same everywhere
    B
    will have the same value everywhere but not directed towards the centre
    C
    will be same everywhere in magnitude directed towards the same
    D
    cannot be zero at any point

  • Assuming the earth to be a sphere of uniform density, the acceleration due to gravity

    A
    at a point outside the earth is inversely proportional to the square of its distance from the centre
    B
    at a point outside the earth is inversely proportional to its distance from the centre
    C
    at a point inside is zero
    D
    at a point inside is inversely proportional to its distance from the centre.

  • At a height equal to earth's radius, above the earth's surface, the acceleration due to gravity is

    A
    g
    B
    `(g )/(2)`
    C
    `(g )/(4)`
    D
    `g/8`

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