Kepler's laws of Planetary Motion PYQs: JEE Mains Physics

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1. 1. A planet \((P_1)\) is moving around the star of mass \(2M\) in the orbit of radius \(R\). Another planet \((P_2)\) is moving around another star of mass \(4M\) in a orbit of radius \(2R\). Ratio of time periods of revolution of \(P_2\) and \(P_1\) is _______. 2026 Medium
2. 2. Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
   Assertion (A) : The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.
   Reason (R) : For a central force field the angular momentum is a constant.
   In the light of the above statements, choose the most appropriate answer from the options given below : 2025 Easy
3. 3. Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time \(\mathrm{T}=4\) seconds. If the sides of the triangle are increased to length 2 a and also the masses of the spheres are made 2 m , then they will collide after _____ seconds. 2025 Medium
4. 4. A planet takes \(200\) days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution? 2024 Hard
5. 5. A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is _______. (Given \(=\) Radius of geo-stationary orbit for earth is \(4.2 \times 10^4 \mathrm{~km}\) ) 2024 Hard
6. 6. Given below are two statements: one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\). \(Assertion\) \((A)\) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun. \(Reason\) \((R)\): The moon takes less time to move around the earth than the time taken by the earth to move around the sun. In the light of the above statements, choose the most appropriate answer from the options given below: 2024 Hard
7. 7. Every planet revolves around the sun in an elliptical orbit : \(A.\) The force acting on a planet is inversely proportional to square of distance from sun. \(B.\) Force acting on planet is inversely proportional to product of the masses of the planet and the sun \(C.\) The centripetal force acting on the planet is directed away from the sun. \(D.\) The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit. Choose the correct answer from the options given below : 2023 Medium
8. 8. If the distance of the earth from Sun is \(1.5 \times 10^6\,km\). Then the distance of an imaginary planet from Sun, if its period of revolution is \(2.83\) years is \(.............\times 10^6\,km\) 2023 Medium
9. 9. If the earth suddenly shrinks to \(\frac{1}{64}\) th of its original volume with its mass remaining the same, the period of rotation of earth becomes \(\frac{24}{ x } h\). The value of \(x\) is \(.......\) 2023 Hard
10. 10. The time period of a satellite of earth is \(24\) hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become \(.......\,hours\) 2023 Easy
11. 11. The distance between Sun and Earth is \(R.\) The duration of year if the distance between Sun and Earth becomes \(3R\) will be  2022 Medium
12. 12. The time period of a satellite revolving around earth in a given orbit is \(7 \,hours\). If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be ...... \(hours\) 2022 Medium
13. 13. Two planets \(A\) and \(B\) of equal mass are having their period of revolutions \(T_{A}\) and \(T_{B}\) such that \(T_{A}=2 T_{B}\). These planets are revolving in the circular orbits of radii \(I_{A}\) and \(I_{B}\) respectively. Which out of the following would be the correct relationship of their orbits? 2022 Medium
14. 14. A geostationary satellite is orbiting around an arbitary planet \(^{\prime} P ^{\prime}\) at a height of \(11 R\) above the surface of \(^{\prime} P ^{\prime} ,\) \(R\) being the radius of \(^{\prime} P .^{\prime}\) The time period of another satellite in hours at a height of \(2R\) from the surface of \(^{\prime} P ^{\prime}\) is \(........\).\(^{\prime} P ^{\prime}\) has the time period of \(24\, hours.\) 2021 Medium
15. 15. A planet revolving in elliptical orbit has \((A)\) a constant velocity of revolution. \((B)\) has the least velocity when it is nearest to the sun. \((C)\) its areal velocity is directly proportional to its velocity. \((D)\) areal velocity is inversely proportional to its velocity. \((E)\) to follow a trajectory such that the areal velocity is constant. Choose the correct answer from the options given below 2021 Hard
16. 16. The angular momentum of a planet of mass \(M\) moving around the sun in an elliptical orbit is \(\overrightarrow{ L }\). The magnitude of the areal velocity of the planet is: 2021 Medium
17. 17. The maximum and minimum distances of a comet from the Sun are \(1.6 \times 10^{12}\, m\) and \(8.0 \times 10^{10}\, m\) respectively. If the speed of the comet at the nearest point is \(6 \times 10^{4}\, ms ^{-1},\) the speed at the farthest point is ......... \(\times 10^{3}\, m / s\) 2021 Medium
18. 18. The planet Mars has two moons, if one of them has a period \(7\, hours,\, 30\, minutes\) and an orbital radius of \(9.0 \times 10^{3}\, {km} .\) Find the mass of Mars. \(\left\{\operatorname{Given} \frac{4 \pi^{2}}{G}=6 \times 10^{11} {N}^{-1} {m}^{-2} {kg}^{2}\right\}\) 2021 Medium
19. 19. The time period of a satellite in a circular orbit of radius \(R\) is \(T\). The period of another satellite in a circular orbit of radius \(9 R\) is............ \(T\) 2021 Medium
20. 20. If the angular momentum of a planet of mass \(m\), moving a round the Sun in a circular orbit its \(L\), about the center of the Sun, its areal velocity is 2019 Easy
21. 21. The relative uncertainty in the period of a sateilite orbiting around the earth is \(10^{-2}\). If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is 2018 Medium
22. 22. India's Mangalyan was sent to the Mars by launching it into a transfer orbit \(EOM\) around the sun . It leaves the earth at \(E\) and meets Mars at \(M\) . If the semi-major axis of Earth's orbit is \(a_e = 1.5 \times 10^{11}\, m\), that of Mars orbit \(a_m= 2.28 \times 10^{11}\, m\), taken Kepler's laws give the estimate of time for Mangalyan to reach Mars from Earth to be close to ........ \(days\).
    2014 Hard

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