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Q. No.A satellite is in a circular orbit around a planet, orbiting with a speed of \(2\) km/s. What is the minimum additional velocity that should be given to it, perpendicular to its motion, so that it escapes?
| 1. | \(2\) km/s | 2. | \(2\sqrt2\) km/s |
| 3. | \(2(\sqrt2-1)\) km/s | 4. | \(2(\sqrt2+1)\) km/s |
Subtopic: Â Escape velocity |
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Given below are two statements:
| Statement I: | The gravitational force acting on a particle depends on the electric charge of the particle. |
| Statement II: | The gravitational force on an extended body can be calculated by assuming the body to be a particle 'concentrated' at its centre of mass and applying Newton's law of gravitation. |
| 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: Â Newton's Law of Gravitation |
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A block of mass \(m\) is slowly taken vertically upward over a large distance \(h\) in the earth's gravitational field, starting from its surface. The gravitational field at its final destination is \({\Large\frac{g}{27}},\) where \(g\) is the field at the earth's surface. The work done in the process is:
1. \(mgh\)
2. \(\Large\frac{mgh}{27}\)
3. \(\Large\frac{mgh}{\sqrt{27}}\)
4. \(\Large\frac{14mgh}{27}\)
1. \(mgh\)
2. \(\Large\frac{mgh}{27}\)
3. \(\Large\frac{mgh}{\sqrt{27}}\)
4. \(\Large\frac{14mgh}{27}\)
Subtopic: Â Gravitational Potential Energy |
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Two stars of equal mass rotate about a common centre-of-mass in a common circular orbit of radius \(R.\) The total mass of the stars is \(M.\)
The gravitational force exerted by the stars, on each other, is:
The gravitational force exerted by the stars, on each other, is:
| 1. | \(\Large\frac{GM^2}{4R^2}\) | 2. | \(\Large\frac{GM^2}{R^2}\) |
| 3. | \(\Large\frac{GM^2}{16R^2}\) | 4. | \(\Large\frac{4GM^2}{R^2}\) |
Subtopic: Â Newton's Law of Gravitation |
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Two particles of masses \(M,m\) are separated by a distance \(r.\) Their relative acceleration due to their mutual gravitational forces is (of magnitude):
| 1. | \(\Large\frac{2GMm}{r^2(M+m)}\) | 2. | \(\Large\frac{GMm}{r^2(M+m)}\) |
| 3. | \(\Large\frac{G(M\text - m)}{r^2}\) | 4. | \(\Large\frac{G(M\text + m)}{r^2}\) |
Subtopic: Â Acceleration due to Gravity |
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Two identical-mass planets (mass: \(m\)) move around a Star (mass: \(M\)) in a circular orbit of radius \(r,\) in a symmetrical manner. The orbital speed of the planets is:
1. \(\sqrt{\dfrac{2GM}{r}}\)
2. \(\sqrt{\dfrac{5GM}{4r}}\)
3. \(\sqrt{\dfrac{G(M+m)}{r}}\)
4. \(\sqrt{\dfrac{G[M+(m/4)]}{r}}\)
Subtopic: Â Newton's Law of Gravitation |
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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. | \(h>\dfrac{u^2}{2g}\) |
| 2. | \(h=\dfrac{u^2}{2g}\) |
| 3. | \(h<\dfrac{u^2}{2g}\) |
| 4. | Any of the above may be true, depending on the earth's radius |
Subtopic: Â Acceleration due to Gravity |
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The angular momentum of a planet of mass \(m,\) moving around the sun (mass: \(M\gg m\)) in an orbit of radius \(r\) is proportional to:
| 1. | \(mr\) | 2. | \(\dfrac{m}{r}\) |
| 3. | \(m\sqrt r\) | 4. | \(\dfrac{m}{\sqrt r}\) |
Subtopic: Â Kepler's Laws |
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If the axis of rotation of the earth was extended into the space, then it would pass close to:
1. the moon
2. the sun
3. the pole star
4. the center of mass of all the planets in the solar system
Subtopic: Â Kepler's Laws |
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A point particle of mass \(m\) is placed at the centre \((O)\) of a uniform hemispherical shell of equal mass \(m,\) as shown. A third particle of mass \(m\) is placed at \(A,\) which is at a distance \(2R\) from \(O.\) \(OA\) lies along a diameter of the rim of the hemisphere; \(R\) is its radius. The gravitational potential energy of interaction between \(m~(A)\) and \(m~(O)\) is \(U_1;\) between \(m~(A)\) and \(m\) (hemisphere) is \(U_2\) and; between \(m~(O)\) and \(m\) (hemisphere) is \(U_3.\) Which, of the following, is true?
1. \(|U_1|=|U_2|=|U_3|\)
2. \(|U_2|<|U_1|<|U_3|\)
3. \(|U_1|=|U_2|<|U_3|\)
4. \(|U_3|<|U_1|<|U_2|\)
1. \(|U_1|=|U_2|=|U_3|\)
2. \(|U_2|<|U_1|<|U_3|\)
3. \(|U_1|=|U_2|<|U_3|\)
4. \(|U_3|<|U_1|<|U_2|\)
Subtopic: Â Gravitational Potential Energy |
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