A satellite is moving very close to a planet of density $\mathrm{\rho }$. The time period of the satellite is:

1.  $\sqrt{\frac{3\mathrm{\pi }}{\mathrm{\rho G}}}$

2.  ${\left(\frac{3\mathrm{\pi }}{\mathrm{\rho G}}\right)}^{3/2}$

3.  $\sqrt{\frac{3\mathrm{\pi }}{2\mathrm{\rho G}}}$

4.  ${\left(\frac{3\mathrm{\pi }}{2\mathrm{\rho G}}\right)}^{3/2}$

Concept Questions :-

Kepler laws
NEET 2021 - Achiever Batch - Aryan Raj Singh

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A projectile is fired upwards from the surface of the earth with a velocity ${\mathrm{kv}}_{\mathrm{e}}$ where ${\mathrm{v}}_{\mathrm{e}}$ 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.  $\frac{\mathrm{R}}{{\mathrm{k}}^{2}}$

2.

3.

4.

Concept Questions :-

Escape velocity
NEET 2021 - Achiever Batch - Aryan Raj Singh

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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
NEET 2021 - Achiever Batch - Aryan Raj Singh

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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

Concept Questions :-

Kepler laws
NEET 2021 - Achiever Batch - Aryan Raj Singh

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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.

2. ${R}^{\left(\frac{n+1}{2}\right)}$

3. Rn
4.

Concept Questions :-

Newton law of gravitation

Difficulty Level:

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
NEET 2021 - Achiever Batch - Aryan Raj Singh

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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
NEET 2021 - Achiever Batch - Aryan Raj Singh

Difficulty Level:

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
NEET 2021 - Achiever Batch - Aryan Raj Singh

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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.  $\frac{3}{4}{\mathrm{mv}}^{2}$

2.  $\frac{1}{2}{\mathrm{mv}}^{2}$

3.  $-\frac{1}{2}{\mathrm{mv}}^{2}$

4.  ${\mathrm{mv}}^{2}$

Concept Questions :-

Gravitational potential energy
NEET 2021 - Achiever Batch - Aryan Raj Singh

Difficulty Level:

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