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Q. No.Given below are two statements:
Statement I:
The kinetic energy of a planet is maximum when it is closest to the sun.
Statement II:
The time taken by a planet to move from the closest position (perihelion) to the farthest position (aphelion) is larger for a planet that is farther from the sun.
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.
Subtopic: Kepler's Laws |
71%
From NCERT
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The value of acceleration due to gravity on the surface of a planet is \(\left ( \dfrac{1}{6} \right )\)th that of the earth. The radius of the planet is \(\left ( \dfrac{1}{3} \right )\)rd of earth's radius. What is the escape speed from the surface of the planet?
(Given the escape from the surface of earth is \(v_{e}\) km/s)
(Given the escape from the surface of earth is \(v_{e}\) km/s)
| 1. | \(\sqrt{\dfrac{1}{18}} v_e\) | 2. | \(\sqrt{\dfrac{1}{2}} v_e\) |
| 3. | \(\sqrt{\dfrac{1}{9}} v_e\) | 4. | \(\sqrt{\dfrac{1}{10}} v_e\) |
Subtopic: Escape velocity |
79%
From NCERT
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The variation of intensity of the gravitational field \((E)\) of the moon (having radius \(R\) ) with distance \((r)\) from the centre of the moon is represented by:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Acceleration due to Gravity |
58%
From NCERT
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A satellite of mass \(M\) is revolving around the Earth in a stationary orbit with a time period \(T.\) If \(10\%\) of the satellite's mass is detached, what will happen to its time period?
1. remain the same
2. increase by \(10\%\)
3. decrease by \(10\%\)
4. decrease by \(20\%\)
Subtopic: Satellite |
81%
From NCERT
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Four particles, each of mass \(m,\) are kept at the four corners of a square of side \(l\) each. The amount of work done to separate these particles for no interaction between them will be:
1. \(\dfrac{4Gm^2}{l}\)
2. \(-{\dfrac{Gm^2} {l}}(4+\sqrt 2)\)
3. \({\dfrac{Gm^2}{l}}(4+\sqrt 2)\)
4. \(\dfrac{{Gm}^2}{l}\left(1+\dfrac{1}{\sqrt{2}}\right)\)
1. \(\dfrac{4Gm^2}{l}\)
2. \(-{\dfrac{Gm^2} {l}}(4+\sqrt 2)\)
3. \({\dfrac{Gm^2}{l}}(4+\sqrt 2)\)
4. \(\dfrac{{Gm}^2}{l}\left(1+\dfrac{1}{\sqrt{2}}\right)\)
Subtopic: Gravitational Potential |
From NCERT
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Two planets \(A\) and \(B\) of equal masses are having their periods of revolution \(T_{A}\) and \(T_{B}\) such that \(T_{A}=2 {T}_{B}\). These planets are revolving in the circular orbits of radii \({r}_{A}\) and \(r_{B}\) respectively. Which of the following would be the correct relationship of their orbits?
1. \(2 r_{A}^2=r_{B}^2 \)
2. \(r_{A}^3=2 r_{B}^3 \)
3. \(r_{A}^3=4{r}_{B}^3 \)
4. \(T_{A}^2-{T}_{B}^2=\dfrac{\pi^2}{GM}\left({r}_{B}^3-4 {r}_{A}^3\right)\)
1. \(2 r_{A}^2=r_{B}^2 \)
2. \(r_{A}^3=2 r_{B}^3 \)
3. \(r_{A}^3=4{r}_{B}^3 \)
4. \(T_{A}^2-{T}_{B}^2=\dfrac{\pi^2}{GM}\left({r}_{B}^3-4 {r}_{A}^3\right)\)
Subtopic: Kepler's Laws |
78%
From NCERT
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The percentage decrease in the weight of a rocket, when it is taken to a height of \(32~\text{km}\) above the surface of the earth will be:
(the radius of the Earth \(R=6400~\text{km}\))
1. \(1\text{%}\)
2. \(3\text{%}\)
3. \(4\text{%}\)
4. \(0.5\text{%}\)
(the radius of the Earth \(R=6400~\text{km}\))
1. \(1\text{%}\)
2. \(3\text{%}\)
3. \(4\text{%}\)
4. \(0.5\text{%}\)
Subtopic: Acceleration due to Gravity |
85%
From NCERT
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A body weighs \(72\) N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth from the surface?
| 1. | \(72\) N | 2. | \(32\) N |
| 3. | \(28\) N | 4. | \(16\) N |
Subtopic: Acceleration due to Gravity |
88%
From NCERT
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The radius of a planet is twice the radius of the Earth. Both have almost equal average mass densities. If \(v_P\) and \(v_E\) are escape velocities of the planet and the earth, respectively, then:
1. \(v_P = 1.5 v_E\)
2. \(v_P = 2v_E\)
3. \(v_E = 3 v_P\)
4. \(v_E = 1.5v_P\)
1. \(v_P = 1.5 v_E\)
2. \(v_P = 2v_E\)
3. \(v_E = 3 v_P\)
4. \(v_E = 1.5v_P\)
Subtopic: Escape velocity |
79%
From NCERT
NEET - 2013
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A particle of mass \(m\) is kept at rest at a height \(3R\) from the surface of the Earth, where \(R\) is the radius of the Earth and \(M\) is the mass of the Earth. The minimum speed with which it should be projected, so that it does not return, is:
(where \(g\) is the acceleration due to gravity on the surface of the Earth)
(where \(g\) is the acceleration due to gravity on the surface of the Earth)
| 1. | \(\left(\dfrac{{GM}}{2 {R}}\right)^{\frac{1}{2}} \) | 2. | \(\left(\dfrac{{g} R}{4}\right)^{\frac{1}{2}} \) |
| 3. | \( \left(\dfrac{2 g}{R}\right)^{\frac{1}{2}} \) | 4. | \(\left(\dfrac{G M}{R}\right)^{\frac{1}{2}}\) |
Subtopic: Escape velocity |
74%
From NCERT
NEET - 2013
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