Q. No.Initially a satellite of \(100~\text{kg}\) is in a circular orbit of radius \(1.5R_E\). This satellite can be moved to a circular orbit of radius \(3R_E\) by supplying \(\alpha \times 10^{6}~\text{J}\) of energy. The value of \(\alpha\) is:
(Take Radius of Earth \(R_E = 6\times 10^{6}~\text{m}\) and \(g = 10~\text{m/s}^2\))
1. \(150\)
2. \(500\)
3. \(100\)
4. \(1000\)
(Take Radius of Earth \(R_E = 6\times 10^{6}~\text{m}\) and \(g = 10~\text{m/s}^2\))
1. \(150\)
2. \(500\)
3. \(100\)
4. \(1000\)
Subtopic: Satellite |
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Given below are two statements:
In the light of the above statements, choose the correct answer from the options given below:
| Statement I: | A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth. |
| Statement II: | The time period of revolution of the satellite is \(T=2 \pi\sqrt{\dfrac{R_e}{g}}\) (for satellite very close to the earth surface), where \(R_e\) radius of earth and \(g\) acceleration due to gravity. |
| 1. | Both Statement I and Statement II are False |
| 2. | Both Statement I and Statement II are True |
| 3. | Statement I is True but Statement II is False |
| 4. | Statement I is False but Statement II is True |
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Two planets, \(A\) and \(B\) are orbiting a common star in circular orbits of radii \(R_A\) and \(R_B \) respectively, with \(R_B = 2R_A \). The planet \(B\) is \(4 \sqrt{2} \) times more massive than planet \(A.\) The ratio \((L_B/L_A )\) of angular momentum of planet \(B \) to that of planet \(A\) is: (closest to integer)
1. \(2\)
2. \(4\)
3. \(8\)
4. \(16\)
1. \(2\)
2. \(4\)
3. \(8\)
4. \(16\)
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The correct formula for the height of a satellite from Earth's surface is:
1. \(\left(\dfrac{{T}^2 {R}^2 {g}}{4 \pi^2}\right)^{1 / 3}-{R} \)
2. \(\left(\dfrac{T^2 R^2 g}{4 \pi}\right)^{1 / 2}-R \)
3. \(\left(\dfrac{{T}^2 {R}^2}{4 \pi^2 {g}}\right)^{1 / 3}-{R}\)
4. \(\left(\dfrac{{T}^2 {R}^2 {g}}{4 \pi}\right)^{-1 / 3}+{R}\)
1. \(\left(\dfrac{{T}^2 {R}^2 {g}}{4 \pi^2}\right)^{1 / 3}-{R} \)
2. \(\left(\dfrac{T^2 R^2 g}{4 \pi}\right)^{1 / 2}-R \)
3. \(\left(\dfrac{{T}^2 {R}^2}{4 \pi^2 {g}}\right)^{1 / 3}-{R}\)
4. \(\left(\dfrac{{T}^2 {R}^2 {g}}{4 \pi}\right)^{-1 / 3}+{R}\)
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A satellite of \(103\) kg mass is revolving in circular orbit of radius \(2\)R. If
1. \(2.5\) R
2. \(6\) R
3. \(3\) R
4. \(4\) R
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An astronaut takes a ball of mass m from earth to space. He throws the ball into a circular orbit about earth at an altitude of \(318.5\) km. From earth's surface to the orbit, the change in total mechanical energy of the ball is \(x \frac{\mathrm{GM}_{\mathrm{e}} \mathrm{~m}}{21 \mathrm{R}_{\mathrm{e}}}\). The value of \(x\) is (take \(R_e\text { = } 6370\) km) :
1. \(11\)
2. \(10\)
3. \(9\)
4. \(12\)
1. \(11\)
2. \(10\)
3. \(9\)
4. \(12\)
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The correct relation between kinetic energy \((K.E)\) and the total energy \((T.E) \) of a satellite orbiting around the planet is:
1. \(K . E=|T . E|\)
2. \(K .E=2|T . E|\)
3. \(K . E=\dfrac{|T . E|}{2}\)
4. \(|T . E|=3 K . E\)
1. \(K . E=|T . E|\)
2. \(K .E=2|T . E|\)
3. \(K . E=\dfrac{|T . E|}{2}\)
4. \(|T . E|=3 K . E\)
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Given below are two statements:
| Statement I: | If total energy of a satellite revolving around earth in circular path is \(E\), then potential energy of satellite is \(2E.\) |
| Statement II: | Kinetic energy is also twice of total energy. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
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If the time period for one revolution by satellite near the Earth’s surface is \(T,\) then, the time period of revolution of the satellite at a height equal to the radius of the Earth will be:
| 1. | \(\sqrt 8 ~T\) | 2. | \(\sqrt 2 ~T\) |
| 3. | \(\sqrt 4 ~T\) | 4. | \(\sqrt 3 ~T\) |
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Suppose a situation in which two planet orbits around the sun in same orbit. If the mass of planet 1 is twice the mass of planet 2, then what do they have same?
1. Potential energy
2. Kinetic energy
3. Total energy
4. Velocity
1. Potential energy
2. Kinetic energy
3. Total energy
4. Velocity
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