Q. No.Starting from the centre of the earth, having radius \(R,\) the variation of \(g\) (acceleration due to gravity) is shown by:
1.
2.
3.
4.
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. | \(\dfrac{mg_0R^2}{2(R+h)}\) | 2. | \(-\dfrac{mg_0R^2}{2(R+h)}\) |
| 3. | \(\dfrac{2mg_0R^2}{(R+h)}\) | 4. | \(-\dfrac{2mg_0R^2}{(R+h)}\) |
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. \(K_B >K_A> K_C\)
(Take, the radius of the earth as \(6400~\text{km}\))
2. \(1400~\text{km}\)
3. \(2000~\text{km}\)
4. \(2600~\text{km}\)
1. \(1:2\sqrt{2}\)
2. \(1:4\)
3. \(1:\sqrt{2}\)
4. \(1:2\)
A remote sensing satellite of the 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. |
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