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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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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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 |
 63%
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NEET - 2022
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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 |
 81%
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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 |
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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 |
 84%
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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 |
 68%
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