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Question
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.
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Solution
Gravitational potential is same at all point in a spherical shell. So, the intensity which is negative of gravitational potential gradient is zero. Thus, the gravitational force acting on any particle at any point inside the spherical shell is symmetrical.
In the given figure, the upper half of a spherical shell is cut out. So, the net gravitational force on a particle at the centre of the sphere will be downward.
As the gravitational force per unit mass is the intensity therefore, the direction of gravitational intensity will also be downward that is along c.
Thus, option (iii) is correct.
Gravitational potential is same at all point in a spherical shell. So, the intensity which is negative of gravitational potential gradient is zero. Thus, the gravitational force acting on any particle at any point inside the spherical shell is symmetrical.
In the given figure, the upper half of a spherical shell is cut out. So, the net gravitational force on a particle at the centre of the sphere will be downward.
As the gravitational force per unit mass is the intensity therefore, the direction of gravitational intensity will also be downward that is along c.
Thus, option (iii) is correct.
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