A satellite is moving very close to a planet of density ρ. The time period of the satellite is:

1.  3πρG

2.  3πρG3/2

3.  3π2ρG

4.  3π2ρG3/2

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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.  Rk2

2.  R1 - k2

3.  2R1 - k2

4.  2R1 + k2

Concept Questions :-

Escape velocity
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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

Concept Questions :-

Gravitational Potential
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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 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

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Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of revolution of a planet in a circular orbit of radius R around the sun will be proportional to

1. Rn-12  

2. Rn+12

3. Rn
4.   R(n-2)2

Concept Questions :-

Newton law of gravitation
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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

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If A is the areal velocity of a planet of mass M, its angular momentum is

1.  MA

2.  2MA

3.  A2M

4.  AM2

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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

Concept Questions :-

Gravitational Potential
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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

Concept Questions :-

Gravitational potential energy
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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

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