A ''double star'' is a composite system of two stars rotating about their center of mass under their mutual gravitational attraction. Let us consider such a ''double star'' which has two stars of masses 'm' and '2m' at a separation '1'. If T is the time period of rotation about their enter of mass then.
- $T=2\pi\sqrt\frac{l^3}{mG}$
- $T=2\pi\sqrt\frac{l^3}{2mG}$
- $T=2\pi\sqrt\frac{l^3}{3mG}$
- $T=2\pi\sqrt\frac{l^3}{4mG}$
The Correct Option is C
Solution and Explanation
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Net gravitational force at the center of a square is found to be \( F_1 \) when four particles having masses \( M, 2M, 3M \) and \( 4M \) are placed at the four corners of the square as shown in figure, and it is \( F_2 \) when the positions of \( 3M \) and \( 4M \) are interchanged. The ratio \( \dfrac{F_1}{F_2} = \dfrac{\alpha}{\sqrt{5}} \). The value of \( \alpha \) is
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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].