8.10 In the following two exercises, choose the correct answer from among the given ones:
The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow (see Fig 8.12) (i) a (ii) b (iii) c (iv) 0
Gravitational potential (V) is constant at all points in a spherical shell. Hence the gravitational gradient ( is zero everywhere inside the spherical shell. The gravitational potential gradient is equal to the negative of gravitational intensity. Hence intensity is also zero at all points inside the spherical shell. This indicates that gravitational forces acting at a point in a spherical shell are symmetric
If the upper half of a spherical shell is cut out then the net gravitational force acting on a particle located at the centre O will be in the downward direction
Since gravitational intensity at a point is defined as the gravi
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Gravitational potential (V) is constant at all points in a spherical shell. Hence the gravitational gradient ( is zero everywhere inside the spherical shell. The gravitational potential gradient is equal to the negative of gravitational intensity. Hence intensity is also zero at all points inside the spherical shell. This indicates that gravitational forces acting at a point in a spherical shell are symmetric
If the upper half of a spherical shell is cut out then the net gravitational force acting on a particle located at the centre O will be in the downward direction
Since gravitational intensity at a point is defined as the gravitational force per unit mass at that point, it will also act in the downward direction. Thus the gravitational intensity at centre O of the given hemispherical shell has the direction as indicated by arrow c.
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<p>Gravitational potential (V) is constant at all points in a spherical shell. Hence the gravitational gradient ( <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mi>d</mi><mi>V</mi></mrow></mrow><mrow><mrow><mi>d</mi><mi>r</mi></mrow></mrow></mfrac><mo>)</mo><mi></mi></math></span> is zero everywhere inside the spherical shell. The gravitational potential gradient is equal to the negative of gravitational intensity. Hence intensity is also zero at all points inside the spherical shell. This indicates that gravitational forces acting at a point in a spherical shell are symmetric</p><p>If the upper half of a spherical shell is cut out then the net gravitational force acting on a particle located at the centre O will be in the downward direction</p><p>Since gravitational intensity at a point is defined as the gravitational force per unit mass at that point, it will also act in the downward direction. Thus the gravitational intensity at centre O of the given hemispherical shell has the direction as indicated by arrow c.</p>
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