A satellite whose mass is m, is revolving in a circular orbit of radius r, around the earth of mass M. Time of revolution of the satellite is:

1. $\mathrm{T}\propto \frac{{\mathrm{r}}^{5}}{\mathrm{GM}}$

2. $\mathrm{T}\propto \sqrt{\frac{{\mathrm{r}}^{3}}{\mathrm{GM}}}$

3. $\mathrm{T}\propto \sqrt{\frac{\mathrm{r}}{{\mathrm{GM}}^{2}/3}}$

4. $\mathrm{T}\propto \sqrt{\frac{{\mathrm{r}}^{3}}{{\mathrm{GM}}^{2}/4}}$

Subtopic:  Kepler's Laws |
81%
From NCERT
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

The distance of a planet from the sun is $$5$$ times the distance between the earth and the sun. The time period of the planet is:

 1 $$5^{3/2}$$ years 2 $$5^{2/3}$$ years 3 $$5^{1/3}$$ years 4 $$5^{1/2}$$ years

Subtopic:  Kepler's Laws |
80%
From NCERT
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

A planet moves around the sun. At a point P, it is closest to the sun at a distance $$d_1$$ and has speed $$v_1.$$ At another point Q, when it is farthest from the sun at distance $$d_2,$$ its speed will be:

 1 $$d_2v_1 \over d_1$$ 2 $$d_1v_1 \over d_2$$ 3 $$d_1^2v_1 \over d_2$$ 4 $$d_2^2v_1 \over d_1$$
Subtopic:  Kepler's Laws |
81%
From NCERT
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

A satellite that is geostationary in a particular orbit is taken to another orbit. Its distance from the centre of the earth in the new orbit is $$2$$ times that of the earlier orbit. The time period in the second orbit is:
1. $$48$$$\sqrt{2}$ hr
2. $$48$$ hr
3. $$24$$$\sqrt{2}$ hr
4. $$24$$ hr

Subtopic:  Kepler's Laws |
74%
From NCERT
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

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%
From NCERT
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

Kepler's third law states that the square of the period of revolution ($$T$$) of a planet around the sun, is proportional to the third power of average distance $$r$$ between the sun and planet i.e. $$T^2 = Kr^3$$, here $$K$$ is constant. If the masses of the sun and planet are $$M$$ and $$m$$ respectively, then as per Newton's law of gravitation, the force of attraction between them is $$F = \frac{GMm}{r^2},$$ here $$G$$ is the gravitational constant. The relation between $$G$$ and $$K$$ is described as:
1. $$GK = 4\pi^2$$
2. $$GMK = 4\pi^2$$
3. $$K =G$$
4. $$K = \frac{1}{G}$$

Subtopic:  Kepler's Laws |
79%
From NCERT
NEET - 2015
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

The figure shows the elliptical orbit of a planet $$m$$ about the sun $$\mathrm{S}.$$ The shaded area $$\mathrm{SCD}$$ is twice the shaded area $$\mathrm{SAB}.$$ If $$t_1$$ is the time for the planet to move from $$\mathrm{C}$$ to $$\mathrm{D}$$ and $$t_2$$ is the time to move from $$\mathrm{A}$$ to $$\mathrm{B},$$ then:

 1 $$t_1>t_2$$ 2 $$t_1=4t_2$$ 3 $$t_1=2t_2$$ 4 $$t_1=t_2$$

Subtopic:  Kepler's Laws |
71%
From NCERT
AIPMT - 2009
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

If R is the radius of the orbit of a planet and T is the time period of the planet, then which of the following graphs correctly shows the motion of a planet revolving around the sun?

 1 2 3 4

Subtopic:  Kepler's Laws |
78%
From NCERT
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

If two planets are at mean distances ${d}_{1}$ and ${d}_{2}$ from the sun and their frequencies are n1 and n2 respectively, then:

1. ${{n}_{1}}^{2}{{d}_{1}}^{2}={n}_{2}{{d}_{2}}^{2}$

2. ${{n}_{2}}^{2}{{d}_{2}}^{3}={{n}_{1}}^{2}{{d}_{1}}^{3}$

3. ${n}_{1}{{d}_{1}}^{2}={n}_{2}{{d}_{2}}^{2}$

4. ${{n}_{1}}^{2}{d}_{1}={{n}_{2}}^{2}{d}_{2}$

Subtopic:  Kepler's Laws |
66%
From NCERT
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

The time period of a geostationary satellite is 24 h, at a height of 6${R}_{E}$ (${R}_{E}$ is the radius of the earth) from the surface of the earth. The time period of another satellite whose height is 2.5${R}_{E}$ from the surface will be:

1. 6$\sqrt{2}h$

2. 12$\sqrt{2}h$

3. $\frac{24}{2.5}h$

4.  $\frac{12}{2.5}h$

Subtopic:  Kepler's Laws |
67%
From NCERT
NEET - 2019
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints