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Question
Choose the correct answer from among the given ones:
The gravitational intensity at the center of a hemispherical shell of uniform mass density has the direction indicated by the arrow in the above figure.
Choose the correct answer from among the given ones:
The gravitational intensity at the center of a hemispherical shell of uniform mass density has the direction indicated by the arrow in the above figure.
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Solution
The correct option is B c
A hemisphere can be considered to be made up of many infinitesimally thin concentric rings. Figure shows cross-section of a hemisphere of a radius r. It is composed of many rings of radius x where 0<x<r. Gravitational intensity due to a small ring of radius x is →dg as shown in the figure. Gravitational intensity due to all rings =∫dg^j. In other words, total gravitational intensity is the integral of gravitational intensity of all infinitesimally small rings which is in the upward direction.
Therefore for the given figure, the gravitational intensity will be towards (c).
A hemisphere can be considered to be made up of many infinitesimally thin concentric rings. Figure shows cross-section of a hemisphere of a radius r. It is composed of many rings of radius x where 0<x<r. Gravitational intensity due to a small ring of radius x is →dg as shown in the figure. Gravitational intensity due to all rings =∫dg^j. In other words, total gravitational intensity is the integral of gravitational intensity of all infinitesimally small rings which is in the upward direction.
Therefore for the given figure, the gravitational intensity will be towards (c).
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