Magnitude of potential energy (U) and time period (T) of a satellite are related to each other as:

1. T2 α 1U3

2. T α 1U3

3. T2 α U3

4. T2 α 1U2

Subtopic:  Satellite |
 59%
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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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Kepler's second law regarding constancy of the areal velocity of a planet is a consequence of the law of conservation of:

1. Energy

2. Linear momentum

3. Angular momentum

4. Mass

Subtopic:  Kepler's Laws |
 83%
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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. 2GMa

2. 2GMa1-12

3. 2GMa2-1

4. zero

Subtopic:  Gravitational Potential Energy |
 53%
From NCERT
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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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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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In planetary motion, the areal velocity of the position vector of a planet depends on the angular velocity (ω) and the distance of the planet from the sun (r). The correct relation for areal velocity is:

1. dAdt α ωr

2. dAdt α ω2r

3. dAdt α ωr2

4. dAdt α ωr

Subtopic:  Kepler's Laws |
 55%
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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 kve where ve 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 |
 64%
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