# The figure shows a planet in an elliptical orbit around the sun ($$S$$). The ratio of the momentum of the planet at point $$A$$ to that at point $$B$$ is:                                1. $$\frac{r_1}{r_2}$$ 2. $$\frac{r_{1}^{2}}{r_{2}^{2}}$$ 3. $$\frac{r_2}{r_1}$$ 4. $$\frac{r_{2}^{2}}{r_{1}^{2}}$$

Subtopic:  Kepler's Laws |
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Three identical point masses, each of mass $$1$$ kg lie at three points $$(0,0)$$, $$(0,0.2~\text{m})$$, $$(0.2~\text{m}, 0)$$. The net gravitational force on the mass at the origin is:
1. $$6.67\times 10^{-9}(\hat i +\hat j)~\text{N}$$
2. $$1.67\times 10^{-9}(\hat i +\hat j) ~\text{N}$$
3. $$1.67\times 10^{-9}(\hat i -\hat j) ~\text{N}$$
4. $$1.67\times 10^{-9}(-\hat i -\hat j) ~\text{N}$$

Subtopic:  Newton's Law of Gravitation |
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Two particles of mass $$m$$ and $$4m$$ are separated by a distance $$r.$$ Their neutral point is at:
1. $$\frac{r}{2}~\text{from}~m$$
2. $$\frac{r}{3}~\text{from}~4m$$
3. $$\frac{r}{3}~\text{from}~m$$
4. $$\frac{r}{4}~\text{from}~4m$$

Subtopic:  Newton's Law of Gravitation |
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A body of mass $$m$$ is situated at a distance $$4R_e$$ above the Earth's surface, where $$R_e$$ is the radius of the Earth. What minimum energy should be given to the body so that it may escape?
 1 $$mgR_e$$ 2 $$2mgR_e$$ 3 $$\frac{mgR_e}{5}$$ 4 $$\frac{mgR_e}{16}$$
Subtopic:  Gravitational Potential Energy |
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Two satellites $$S_1$$ and $$S_2$$ are revolving around a planet in coplanar and concentric circular orbits of radii $$R_1$$ and $$R_2$$ in the same direction respectively. Their respective periods of revolution are $$1$$ hr and $$8$$ hr. The radius of the orbit of satellite $$S_1$$ is equal to $$10^4$$ km. Find the relative speed when they are closest to each other.
1. $$2\pi \times 10^4~\text{kmph}$$
2. $$\pi \times 10^4~\text{kmph}$$
3. $$\frac{\pi}{2} \times 10^4~\text{kmph}$$
4. $$\frac{\pi}{3} \times 10^4~\text{kmph}$$

Subtopic:  Kepler's Laws |
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The gravitational potential energy of an isolated system of three particles, each of mass $$m$$ placed at three corners of an equilateral triangle of side $$l$$ is:
 1 $$-Gm \over {l}^2$$ 2 $$-Gm^2 \over 2{l}$$ 3 $$-2Gm^2 \over {l}$$ 4 $$-3Gm^2 \over {l}$$
Subtopic:  Gravitational Potential Energy |
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If $$R$$ is the radius of the orbit of a planet and $$T$$ is the time period of the planet, then which of the following graphs correctly shows the motion of a planet revolving around the sun?

 1 2 3 4
Subtopic:  Kepler's Laws |
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A satellite of mass $$m$$ revolving around the earth in a circular orbit of radius $$r$$ has its angular momentum equal to $$L$$ about the centre of the earth. The potential energy of the satellite is:
1. $$- \frac{L^{2}}{2 mr}$$
2. $$- \frac{2L^{2}}{mr^2}$$
3. $$- \frac{3L^{2}}{m^2r^2}$$
4. $$- \frac{L^{2}}{mr^2}$$

Subtopic:  Satellite |
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The value of acceleration due to gravity at a height of $$800$$ km from the surface of the earth (radius of the earth is $$6400$$ km and value of acceleration due to gravity on the earth's surface is $$981$$ cm/${\mathrm{s}}^{2}$) is:
 1 $$775 ~\text{cm/s}^2$$ 2 $$872 ~\text{cm/s}^2$$ 3 $$981 ~\text{cm/s}^2$$ 4 $$\text{zero}$$
Subtopic:  Acceleration due to Gravity |
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A planet is revolving around a massive star in a circular orbit of radius $$R$$. If the gravitational force of attraction between the planet and the star is inversely proportional to $$R^3,$$ then the time period of revolution $$T$$ is proportional to:
1. $$R^5$$
2. $$R^3$$
3. $$R^2$$
4. $$R$$

Subtopic:  Satellite |
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