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 in the below figure.
- a
- b
- c
- o
The Correct Option is C
Solution and Explanation
To determine the direction of gravitational intensity at the center of a hemispherical shell of uniform mass density, we must consider the symmetrical distribution of mass around the center.
The gravitational intensity (\( \mathbf{g} \)) at a point due to a mass is directed towards the mass since it is an attractive force. In this scenario, the hemispherical shell is symmetric about the center.
For a complete spherical shell, the intensity at the center is zero due to symmetry. However, in the case of a hemispherical shell, the symmetry is broken. The net gravitational field will be directed towards the base of the hemisphere, as the top portion of the sphere, which is missing, does not exert any field.
Thus, for a hemispherical shell, the gravitational intensity at the center is along the axis perpendicular to the base and towards the base of the hemisphere.
Based on the given diagram and the options, the direction of the gravitational intensity at the center (point O) is downward, indicated by option c.
Hence, the correct answer is: c.
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Concepts Used:
Gravitation
In mechanics, the universal force of attraction acting between all matter is known as Gravity, also called gravitation, . It is the weakest known force in nature.
Newton’s Law of Gravitation
According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,
- F ∝ (M1M2) . . . . (1)
- (F ∝ 1/r2) . . . . (2)
On combining equations (1) and (2) we get,
F ∝ M1M2/r2
F = G × [M1M2]/r2 . . . . (7)
Or, f(r) = GM1M2/r2
The dimension formula of G is [M-1L3T-2].