In planetary motion, the areal velocity of the position vector of a planet depends on the angular velocity \((\omega)\) and the distance of the planet from the sun \((r)\). The correct relation for areal velocity is:
1. \(\frac{dA}{dt}\propto \omega r\)
2. \(\frac{dA}{dt}\propto \omega^2 r\)
3. \(\frac{dA}{dt}\propto \omega r^2\)
4. \(\frac{dA}{dt}\propto \sqrt{\omega r}\)

Subtopic:  Kepler's Laws |
 57%
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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 |
 74%
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Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is

1.  -5Gmr

2.  -6Gmr

3.  -9Gmr

4.  0

Subtopic:  Gravitational Field |
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The satellite of mass m orbiting around the earth in a circular orbit with a velocity v. The total energy will be:

1.  34mv2

2.  12mv2

3.  -12mv2

4.  mv2

Subtopic:  Gravitational Potential Energy | Escape velocity |
 77%
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A projectile fired vertically upwards with a speed v escapes from the earth. If it is to be fired at 45° to the horizontal, what should be its speed so that it escapes from the earth?

1.  v

2.  v2

3.  2v

4.  2v

Subtopic:  Escape velocity |
 58%
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A body of super dense material with mass twice the mass of the earth but size very small compared to size of the earth starts from rest from h<<R above the Earth's surface. It reaches earth in time t:

1. t=hg

2. t=2hg

3. t=2h3g

4. t=4h3g

Subtopic:  Acceleration due to Gravity |
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A point \(P\) lies on the axis of a ring of mass \(M\) and radius \(a\) at a distance \(a\) from its centre \(C\). A small particle starts from \(P\) and reaches \(C\) under gravitational attraction. Its speed at \(C\) will be:
1. \(\sqrt{\frac{2 GM}{a}}\)
2. \(\sqrt{\frac{2 GM}{a} \left(1 - \frac{1}{\sqrt{2}}\right)}\)
3. \(\sqrt{\frac{2 GM}{a} \left(\sqrt{2} - 1\right)}\)
4. zero

Subtopic:  Gravitational Potential Energy |
 53%
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A planet is moving in an elliptical orbit. If \(T, V, E,\) and \(L\) stand, respectively, for its kinetic energy, gravitational potential energy, total energy and angular momentum about the center of the orbit, then:
1. \(T\) is conserved
2. \(V\) is always positive
3. \(E\) is always negative
4. the magnitude of \(L\) is conserved but its direction changes continuously
Subtopic:  Satellite |
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The gravitational potential difference between the surface of a planet and 10 m above is 5 J/kg. If the gravitational field is supposed to be uniform, the work done in moving a 2 kg mass from the surface of the planet to a height of 8 m is

1.  2J

2.  4J

3.  6J

4.  8J

Subtopic:  Gravitational Potential |
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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 |
 66%
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