- 1(current)
Q. No.If \(A\) is the areal velocity of a planet of mass \(M,\) then its angular momentum is:
| 1. | \(\frac{M}{A}\) | 2. | \(2MA\) |
| 3. | \(A^2M\) | 4. | \(AM^2\) |
The 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. | \(t_1=t_2\) |
Let the speed of the planet at the perihelion \(P\) in figure shown below be \(v_{_P}\) and the Sun-planet distance \(\mathrm{SP}\) be \(r_{_P}.\) Relation between \((r_{_P},~v_{_P})\) to the corresponding quantities at the aphelion \((r_{_A},~v_{_A})\) is:
| 1. | \(v_{_P} r_{_P} =v_{_A} r_{_A}\) | 2. | \(v_{_A} r_{_P} =v_{_P} r_{_A}\) |
| 3. | \(v_{_A} v_{_P} = r_{_A}r_{_P}\) | 4. | none of these |
Which of the following quantities remain constant in a planetary motion (consider elliptical orbits) as seen from the sun?
| 1. | speed |
| 2. | angular speed |
| 3. | kinetic energy |
| 4. | angular momentum |
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:
2. \((4)^{\frac13}T\)
3. \(2T\)
4. \(8T\)
- 1(current)
Q. No.
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