A rocket of mass M is launched vertically from the surface of the earth with an initial speed v. Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is
1.
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If two planets are at mean distances \(d_1\) and \(d_2\) from the sun and their frequencies are \(n_1\) and \(n_2\) respectively, then:
1. \(n^2_1d^2_1= n_2d^2_2\)
2. \(n^2_2d^3_2= n^2_1d^3_1\)
3. \(n_1d^2_1= n_2d^2_2\)
4. \(n^2_1d_1= n^2_2d_2\)
1. | Kepler's law of areas still holds. |
2. | Kepler's law of period still holds. |
3. | Kepler's law of areas and period still hold. |
4. | Neither the law of areas nor the law of period still hold. |
The distance of a planet from the sun is \(5\) times the distance between the earth and the sun. The time period of the planet is:
1. | \(5^{3/2}\) years | 2. | \(5^{2/3}\) years |
3. | \(5^{1/3}\) years | 4. | \(5^{1/2}\) years |
Two satellites A and B go around the earth in circular orbits at heights of respectively from the surface of the earth. Assuming earth to be a uniform sphere of radius , the ratio of the magnitudes of their orbital velocities is:
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2.
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The orbital angular momentum of a satellite revolving at a distance \(r\)from the centre is \(L\). If the distance is increased to 16r, then the new angular momentum will be:
1. | \(16~L\) | 2. | \(64~L\) |
3. | \(L \over 4\) | 4. | \(4~L\) |
A body of mass m kg starts falling from a point 2R above the Earth’s surface. Its kinetic energy when it has fallen to a point ‘R’ above the Earth’s surface, is:
[R - Radius of Earth, M - Mass of Earth, G - Gravitational Constant] -
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A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is:
1. R/3
2. R/2
3. R/4
4. R/5
A satellite is launched into a circular orbit of radius \(R\) around the Earth while a second satellite is launched into an orbit of radius \(1.02~\text{R}\). The percentage difference in the time periods of the two satellites is:
1. | \(0.7\) | 2. | \(1.0\) |
3. | \(1.5\) | 4. | \(3\) |
If the gravitational force between two objects were proportional to \(\frac{1}{R}\) (and not as ) where \(R\) is the separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to:
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4. \(1/R\)