Q. No.The force of gravitation between a particle \(A,\) and another particle \(B\) when separated by a distance \(r\) is \(F_{AB};\) while the force between a particle \(C\) and \(A\) separated by the same distance is \(4F_{AB}.\) The ratio of the masses of \(B\) and \(C\) is:
1. \(4\)
2. \(2\)
3. \(\frac12\)
4. \(\frac14\)
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. | \(2\) km/s | 2. | \(2\sqrt2\) km/s |
| 3. | \(2(\sqrt2-1)\) km/s | 4. | \(2(\sqrt2+1)\) km/s |
| 1. | \(\dfrac{Rc^2}{G}\) | 2. | \(\dfrac{Rc^2}{2G}\) |
| 3. | \(\dfrac{2Rc^2}{G}\) | 4. | \(\sqrt2\dfrac{Rc^2}{G}\) |
| 1. | \(U > mgh\) |
| 2. | \(U < mgh\) |
| 3. | \(U = mgh\) |
| 4. | any of the above may be true depending on the value of \(h,\) considered relative to the radius of the earth. |
| 1. | \(11.2\sqrt2~\text{km/s}\) | 2. | zero |
| 3. | \(11.2~\text{km/s}\) | 4. | \(11.2\sqrt3~\text{km/s}\) |
If a particle is projected vertically upward with a speed \(u,\) and rises to a maximum altitude \(h\) above the earth's surface then:
(\(g=\) acceleration due to gravity at the surface)
| 1. | \(h>\frac{u^2}{2g}\) |
| 2. | \(h=\frac{u^2}{2g}\) |
| 3. | \(h<\frac{u^2}{2g}\) |
| 4. | Any of the above may be true, depending on the earth's radius |
Assume that a space shuttle flies in a circular orbit very close to the earth's surface. Taking the radius of the space shuttle's orbit to be equal to the radius of the earth (\(R\)) and the acceleration due to gravity to be \(g\), the time period of one revolution of the space shuttle is (nearly):
| 1. | \(\sqrt\frac{2R}{g}\) | 2. | \(\sqrt\frac{\pi R}{g}\) |
| 3. | \(\sqrt\frac{2\pi R}{g}\) | 4. | \(\sqrt\frac{4\pi^2 R}{g}\) |
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 satellites A and B move around the earth in the same orbit. The mass of B is twice the mass of A. Then:
| 1. | speeds of A and B are equal. |
| 2. | the potential energy of earth \(+\) A is same as that of earth \(+\) B. |
| 3. | the kinetic energy of A and B are equal. |
| 4. | the total energy of earth \(+\) A is same as that of earth \(+\) B. |
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