Two planets are in a circular orbit of radius \(R\) and \(4R\) about a star. At a specific time, the two planets and the star are in a straight line. If the period of the closest planet is \(T,\) then the star and planets will again be in a straight line after a minimum time:
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & Biology1. | \(6\sqrt{2}~\text{h}\) | 2. | \(12\sqrt{2}~\text{h}\) |
3. | \(\dfrac{24}{2.5}~\text{h}\) | 4. | \(\dfrac{12}{2.5}~\text{h}\) |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyThe kinetic energies of a planet in an elliptical orbit around the Sun, at positions \(A,B~\text{and}~C\) are \(K_A, K_B~\text{and}~K_C\) respectively. \(AC\) is the major axis and \(SB\) is perpendicular to \(AC\) at the position of the Sun \(S\), as shown in the figure. Then:
1. | \(K_A <K_B< K_C\) | 2. | \(K_A >K_B> K_C\) |
3. | \(K_B <K_A< K_C\) | 4. | \(K_B >K_A> K_C\) |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyKepler's third law states that the square of the period of revolution (\(T\)) of a planet around the sun, is proportional to the third power of average distance \(r\) between the sun and planet i.e. \(T^2 = Kr^3\), here \(K\) is constant. If the masses of the sun and planet are \(M\) and \(m\) respectively, then as per Newton's law of gravitation, the force of attraction between them is \(F = \frac{GMm}{r^2},\) here \(G\) is the gravitational constant. The relation between \(G\) and \(K\) is described as:
1. \(GK = 4\pi^2\)
2. \(GMK = 4\pi^2\)
3. \(K =G\)
4. \(K = \frac{1}{G}\)
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyA planet moving along an elliptical orbit is closest to the sun at a distance r1 and farthest away at a distance of r2. If v1 and v2 are the linear velocities at these points respectively, then the ratio is:
1.
2.
3.
4.
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & BiologyThe figure shows the elliptical orbit of a planet \(m\) about the sun \(\mathrm{S}.\) The shaded area \(\mathrm{SCD}\) is twice the shaded area \(\mathrm{SAB}.\) If \(t_1\) is the time for the planet to move from \(\mathrm{C}\) to \(\mathrm{D}\) and \(t_2\) is the time to move from \(\mathrm{A}\) to \(\mathrm{B},\) then:
1. | \(t_1>t_2\) | 2. | \(t_1=4t_2\) |
3. | \(t_1=2t_2\) | 4. | \(t_1=t_2\) |
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NEET MCQ Books for XIth & XIIth Physics, Chemistry & Biology