If $$A$$ is the areal velocity of a planet of mass $$M,$$ then its angular momentum is: 1. $$\frac{M}{A}$$ 2. $$2MA$$ 3. $$A^2M$$ 4. $$AM^2$$

Subtopic:  Kepler's Laws |
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Magnitude of potential energy ($$U$$) and time period ($$T$$) of a satellite are related to each other as:
1. $$T^2\propto \frac{1}{U^{3}}$$
2. $$T\propto \frac{1}{U^{3}}$$
3. $$T^2\propto U^3$$
4. $$T^2\propto \frac{1}{U^{2}}$$

Subtopic:  Satellite |
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A projectile is fired upwards from the surface of the earth with a velocity $$kv_e$$ where $$v_e$$ is the escape velocity and $$k<1$$. If $$r$$ is the maximum distance from the center of the earth to which it rises and $$R$$ is the radius of the earth, then $$r$$ equals:
1. $$\frac{R}{k^2}$$
2. $$\frac{R}{1-k^2}$$
3. $$\frac{2R}{1-k^2}$$
4. $$\frac{2R}{1+k^2}$$

Subtopic:  Escape velocity |
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For the moon to cease as the earth's satellite, its orbital velocity has to be increased by a factor of:

 1 $$2$$ 2 $$\sqrt{2}$$ 3 $$1/\sqrt{2}$$ 4 $$4$$
Subtopic:  Orbital velocity |
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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. $$\frac{R}{\left(\frac{gR}{2v^2}-1\right)}$$
2. $$R\left({\frac{gR}{2v^2}-1}\right)$$
3. $$\frac{R}{\left(\frac{2gR}{v^2}-1\right)}$$
4. $$R{\left(\frac{2gR}{v^2}-1\right)}$$

Subtopic:  Gravitational Potential Energy |
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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. $$n^2_1d_1= n^2_2d_2$$

Subtopic:  Kepler's Laws |
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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

Subtopic:  Kepler's Laws |
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Two satellites $$A$$ and $$B$$ go around the earth in circular orbits at heights of $$R_A ~\text{and}~R_B$$ respectively from the surface of the earth. Assuming earth to be a uniform sphere of radius $$R_e$$${}_{}$, the ratio of the magnitudes of their orbital velocities is:
1. $$\sqrt{\frac{R_{B}}{R_{A}}}$$
2. $$\frac{R_{B} + R_{e}}{R_{A} + R_{e}}$$
3. $$\sqrt{\frac{R_{B} + R_{e}}{R_{A} + R_{e}}}$$
4. $$\left(\frac{R_{A}}{R_{B}}\right)^{2}$$

Subtopic:  Orbital velocity |
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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. $$\frac{R}{3}$$
2. $$\frac{R}{2}$$
3. $$\frac{R}{4}$$
4. $$\frac{R}{5}$$

Subtopic:  Escape velocity |
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If the gravitational force between two objects were proportional to $$\frac{1}{R}$$ (and not as$$\frac{1}{R^2}$$${}^{}$) 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:
1. $$\frac{1}{R^2}$$
2. $$R^{0}$$
3. $$R^{1}$$
4. $$\frac{1}{R}$$

Subtopic:  Orbital velocity |
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