Question:
The distance between two stars of masses 3MS and 6MS is 9R. Here R is the mean distance between the centres of the Earth and the Sun, and MS is the mass of the Sun. The two stars orbit around their common centre of mass in circular orbits with period nT, where T is the period of Earth’s revolution around the Sun. The value of n is ___.
The distance between two stars of masses 3MS and 6MS is 9R. Here R is the mean distance between the centres of the Earth and the Sun, and MS is the mass of the Sun. The two stars orbit around their common centre of mass in circular orbits with period nT, where T is the period of Earth’s revolution around the Sun. The value of n is ___.
Updated On: May 23, 2024
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Correct Answer: 9
Solution and Explanation
\(\begin{array}{l}\left [ 3M_{s}\omega ^{2}\times 6R \right ]=\frac{G(18M^{2}_{s})}{81R^{2}}\end{array}\)
\(\begin{array}{l}\omega ^{2}R = \frac{GM}{81R^{2}}\end{array}\)
\(\begin{array}{l}T^{‘}=\sqrt{\frac{81R^{3}}{GM_{s}}}\end{array}\)
T’ = 9T
n = 9
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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].