Gravitation · JEE Main previous year questions

2021 10 questions

1. Q472021 · 1 Sept 2021 · Shift 2
   
   1. A.$\frac{1}{2}\sqrt{\frac{GM}{R(2\sqrt{2}+1)}}$
   2. B.$\frac{1}{2}\sqrt{\frac{GM}{R}(2\sqrt{2}+1)}$
   3. C.$\frac{1}{2}\sqrt{\frac{GM}{R}(2\sqrt{2}-1)}$
   4. D.$\sqrt{\frac{GM}{R}}$
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   Answer: B

2. Q532021 · 1 Sept 2021 · Shift 2· Numerical answer

   Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hours respectively. The radius of the orbit of nearer satellite is $2\times 10^3\mathrm{km}$. The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is $\frac{\pi }{x}\mathrm{rad}{\mathrm{h}}^{-1}$ where x is ____.

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   Answer: 3

3. Q422021 · 27 Jul 2021 · Shift 2

   Two identical particles of mass 1 kg each go round a circle of radius R, under the action of their mutual gravitational attraction. The angular speed of each particle is :

   1. A.$\sqrt{\frac{G}{2R^3}}$
   2. B.$\frac{1}{2}\sqrt{\frac{G}{R^3}}$
   3. C.$\frac{1}{2R}\sqrt{\frac{1}{G}}$
   4. D.$\frac{2G}{R^3}$
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   Answer: B

4. Q462021 · 27 Jul 2021 · Shift 2

   The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of $9.0\times 10^3\text{ km}$. Find the mass of Mars. $\left\{Given\frac{4{\pi }^2}{G}=6\times 10^{11}{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}\mathrm{k}{\mathrm{g}}^2\right\}$

   1. A.$5.96\times 10^{19}\text{ kg}$
   2. B.$3.25\times 10^{21}\text{ kg}$
   3. C.$7.02\times 10^{25}\text{ kg}$
   4. D.$6.00\times 10^{23}\text{ kg}$
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   Answer: D

5. Q462021 · 25 Jul 2021 · Shift 1

   The minimum and maximum distances of a planet revolving around the sun are $x_1$ and $x_2$. If the minimum speed of the planet on its trajectory is $v_0$ then its maximum speed will be :

   1. A.$\frac{v_0{x}_1^2}{x_2^2}$
   2. B.$\frac{v_0{x}_2^2}{x_1^2}$
   3. C.$\frac{v_0{x}_1}{x_2}$
   4. D.$\frac{v_0{x}_2}{x_1}$
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   Answer: D

6. Q392021 · 25 Jul 2021 · Shift 2

   Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be :

   1. A.2W
   2. B.W
   3. C.$2^{\frac{1}{3}}$W
   4. D.$\sqrt{2}$W
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   Answer: C

7. Q452021 · 18 Mar 2021 · Shift 1

   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 9R is :

   1. A.9 T
   2. B.27 T
   3. C.12 T
   4. D.3 T
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   Answer: B

8. Q442021 · 26 Feb 2021 · Shift 1

   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 :

   1. A.D only
   2. B.E only
   3. C.C only
   4. D.A only
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   Answer: B

9. Q492021 · 26 Feb 2021 · Shift 1
   
   1. A.$\frac{2\sqrt{2}}{3}\cdot \frac{GMm}{R^2}$
   2. B.$\frac{\sqrt{8}}{9}\cdot \frac{GMm}{R}$
   3. C.$\frac{\sqrt{8}}{27}\cdot \frac{GMm}{R^2}$
   4. D.$\frac{1}{3\sqrt{8}}\cdot \frac{GMm}{R^2}$
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   Answer: C

10. Q532021 · 25 Feb 2021 · Shift 2· Numerical answer

    The initial velocity $v_i$ required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity $v_e$ such that $v_i=\sqrt{\frac{x}{y}}\times v_e$. The value of x will be ______ .

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    Answer: 10