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

Concept Questions :-

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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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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

Concept Questions :-

Escape velocity
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Kepler's second law regarding constancy of areal velocity of a planet is a consequence of law of conservation of

(1) Energy

(2) Linear momentum

(3) Angular momentum

(4) Mass

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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

Concept Questions :-

Acceleration due to gravity
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A thin rod of length L is bent to form a semicircle. The mass of the rod is M. The gravitational potential at the centre of the circle is :

1. -GML

2. -GM2πL

3. -πGM2L

4. -πGML

Concept Questions :-

Gravitational Potential
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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

Concept Questions :-

Gravitational potential energy
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