Q. No.A satellite of mass \(m\) is orbiting the earth (of radius \(R\)) at a height \(h\) from its surface. What is the total energy of the satellite in terms of \(g_0?\)
(\(g_0\) is the value of acceleration due to gravity at the earth's surface)
1. \(\frac{mg_0R^2}{2(R+h)}\)
2. \(-\frac{mg_0R^2}{2(R+h)}\)
3. \(\frac{2mg_0R^2}{(R+h)}\)
4. \(-\frac{2mg_0R^2}{(R+h)}\)
(\(g_0\) is the value of acceleration due to gravity at the earth's surface)
1. \(\frac{mg_0R^2}{2(R+h)}\)
2. \(-\frac{mg_0R^2}{2(R+h)}\)
3. \(\frac{2mg_0R^2}{(R+h)}\)
4. \(-\frac{2mg_0R^2}{(R+h)}\)
The acceleration due to gravity at a height \(1~\text{km}\) above the earth's surface is the same as at a depth \(d\) below the surface of the earth. Then:
| 1. | \(d= 1~\text{km}\) | 2. | \(d= \frac{3}{2}~\text{km}\) |
| 3. | \(d= 2~\text{km}\) | 4. | \(d= \frac{1}{2}~\text{km}\) |
Two astronauts are floating in gravitation-free space after having lost contact with their spaceship. The two will:
| 1. | move towards each other. |
| 2. | move away from each other. |
| 3. | become stationary. |
| 4. | keep floating at the same distance between them. |
If the mass of the sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following statements would not be correct?
| 1. | Raindrops would drop faster. |
| 2. | Walking on the ground would become more difficult. |
| 3. | Time period of a simple pendulum on the earth would decrease. |
| 4. | Acceleration due to gravity \((g)\) on earth would not change. |
The 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. | \(K_B >K_A> K_C\) |
2. \(1400\) km
3. \(2000\) km
4. \(2600\) km
1. \(1:2\sqrt{2}\)
2. \(1:4\)
3. \(1:\sqrt{2}\)
4. \(1:2\)
A remote sensing satellite of earth revolves in a circular orbit at a height of \(0.25 \times10^6~\text{m}\) above the surface of the earth. If Earth’s radius is \(6.38\times10^6~\text{m}\) and \(g=9.8~\text{ms}^{-2}\), then the orbital speed of the satellite is:
1. \(7.76~\text{kms}^{-1}\)
2. \(8.56~\text{kms}^{-1}\)
3. \(9.13~\text{kms}^{-1}\)
4. \(6.67~\text{kms}^{-1}\)
A satellite S is moving in an elliptical orbit around the earth. If the mass of the satellite is very small as compared to the mass of the earth, then:
| 1. | The angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant. |
| 2. | The total mechanical energy of S varies periodically with time. |
| 3. | The linear momentum of S remains constant in magnitude. |
| 4. | The acceleration of S is always directed towards the centre of the earth. |
Kepler'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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