# Two planets are in a circular orbit of radius $$R$$ and $$4R$$ about a star. At a specific time, the two planets and the star are in a straight line. If the period of the closest planet is $$T,$$ then the star and planets will again be in a straight line after a minimum time:             1. $$(4)^2T$$ 2. $$(4)^{\frac13}T$$ 3. $$2T$$ 4. $$8T$$

Subtopic:  Kepler's Laws |
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NEET - 2022
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The force of gravitation between a particle $$A,$$ and another particle $$B$$ when separated by a distance $$r$$ is $$F_{AB};$$ while the force between a particle $$C$$ and $$A$$ separated by the same distance is $$4F_{AB}.$$ The ratio of the masses of $$B$$ and $$C$$ is:
1. $$4$$
2. $$2$$
3. $$\frac12$$
4. $$\frac14$$
Subtopic:  Newton's Law of Gravitation |
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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:  Escape velocity |
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What should be the mass of a uniform sphere of radius $$R$$ so that the escape velocity from its surface equals $$c,$$ the velocity of light in vacuum? (Assume Newton's theory of gravitation to hold true)
 1 $$\dfrac{Rc^2}{G}$$ 2 $$\dfrac{Rc^2}{2G}$$ 3 $$\dfrac{2Rc^2}{G}$$ 4 $$\sqrt2\dfrac{Rc^2}{G}$$
Subtopic:  Escape velocity |
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The gravitational potential energy of a particle of mass $$m$$ increases by $$mgh,$$ when it is raised through a height $$h$$ in a uniform gravitational field "$$g$$". If a particle of mass $$m$$ is raised through a height $$h$$ in the earth's gravitational field ($$g$$: the field on the earth's surface) and the increase in gravitational potential energy is $$U$$, then:
 1 $$U > mgh$$ 2 $$U < mgh$$ 3 $$U = mgh$$ 4 any of the above may be true depending on the value of $$h,$$ considered relative to the radius of the earth.
Subtopic:  Gravitational Potential Energy |
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The escape velocity of a body on the earth's surface is $$11.2$$ km/s. If the same body is projected upward with a velocity $$22.4$$ km/s, the velocity of this body at infinite distance from the center of the earth will be:
 1 $$11.2\sqrt2$$ km/s 2 zero 3 $$11.2$$ km/s 4 $$11.2\sqrt3$$ km/s
Subtopic:  Escape velocity |
From NCERT
NEET - 2023
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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 surface)

 1 $$h>\frac{u^2}{2g}$$ 2 $$h=\frac{u^2}{2g}$$ 3 $$h<\frac{u^2}{2g}$$ 4 Any of the above maybe true, depending on the earth's radius
Subtopic:  Acceleration due to Gravity |
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Assume that a space shuttle flies in a circular orbit very close to the earth's surface. Taking the radius of the space shuttle's orbit to be equal to the radius of the earth ($$R$$) and the acceleration due to gravity to be $$g$$, the time period of one revolution of the space shuttle is (nearly):

 1 $$\sqrt\frac{2R}{g}$$ 2 $$\sqrt\frac{\pi R}{g}$$ 3 $$\sqrt\frac{2\pi R}{g}$$ 4 $$\sqrt\frac{4\pi^2 R}{g}$$
Subtopic:  Satellite |
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Which of the following quantities remain constant in a planetary motion (consider elliptical orbits) as seen from the sun?
1. speed
2. angular speed
3. kinetic energy
4. angular momentum

Subtopic:  Kepler's Laws |
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Two satellites A and B move around the earth in the same orbit. The mass of B is twice the mass of A. Then:

 1 speeds of A and B are equal. 2 the potential energy of earth $$+$$ A is same as that of earth $$+$$ B. 3 the kinetic energy of A and B are equal. 4 the total energy of earth $$+$$ A is same as that of earth $$+$$ B.

Subtopic:  Satellite |
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