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

1.  $\frac{3}{4}{\mathrm{mv}}^{2}$

2.  $\frac{1}{2}{\mathrm{mv}}^{2}$

3.  $-\frac{1}{2}{\mathrm{mv}}^{2}$

4.  ${\mathrm{mv}}^{2}$

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)

(2)

(3)

(4)

Concept Questions :-

Kepler laws
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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.  $\frac{\mathrm{v}}{\sqrt{2}}$

3.  $\sqrt{2}\mathrm{v}$

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

Concept Questions :-

Kepler laws
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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. $t=\sqrt{\frac{h}{g}}$

2. $t=\sqrt{\frac{2h}{g}}$

3. $t=\sqrt{\frac{2h}{3g}}$

4. $t=\sqrt{\frac{4h}{3g}}$

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. $-\frac{\mathrm{GM}}{\mathrm{L}}$

2. $-\frac{\mathrm{GM}}{2\mathrm{\pi L}}$

3. $-\frac{\mathrm{\pi GM}}{2\mathrm{L}}$

4. $-\frac{\mathrm{\pi GM}}{\mathrm{L}}$

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. $\sqrt{\frac{2\mathrm{GM}}{\mathrm{a}}}$

2. $\sqrt{\frac{2\mathrm{GM}}{\mathrm{a}}\left(1-\frac{1}{\sqrt{2}}\right)}$

3. $\sqrt{\frac{2\mathrm{GM}}{\mathrm{a}}\left(\sqrt{2}-1\right)}$

4. zero

Concept Questions :-

Gravitational potential energy
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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.  $-\frac{5\mathrm{Gm}}{\mathrm{r}}$

2.  $-\frac{6\mathrm{Gm}}{\mathrm{r}}$

3.  $-\frac{9\mathrm{Gm}}{\mathrm{r}}$

4.  0

Concept Questions :-

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

1.  $\frac{\mathrm{M}}{\mathrm{A}}$

2.  2MA

3.  ${\mathrm{A}}^{2}M$

4.  ${\mathrm{AM}}^{2}$

Concept Questions :-

Kepler laws
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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)

(2)

(3)

(4)

Concept Questions :-

Kepler laws
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Difficulty Level: