Gravitation · JEE Main previous year questions

2023 21 questions

1. Q332023 · 13 Apr 2023 · Shift 1

   A planet having mass $9{\mathrm{M}}_e$ and radius $4{\mathrm{R}}_e$, where ${\mathrm{M}}_e$ and ${\mathrm{R}}_e$ are mass and radius of earth respectively, has escape velocity in $\text{km/s}$ given by: (Given escape velocity on earth ${\mathrm{V}}_e=11.2\times 10^3\text{ m/s}$ )

   1. A.$33.6$
   2. B.$11.2$
   3. C.$16.8$
   4. D.$67.2$
   Show answer

   Answer: C

2. Q322023 · 13 Apr 2023 · Shift 2

   Given below are two statements: Statement I : For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases. Statement II : Escape velocity is independent of the radius of the planet. In the light of above statements, choose the most appropriate answer form the options given below

   1. A.Both Statement I and Statement II are correct
   2. B.Statement I is correct but statement II is incorrect
   3. C.Both Statement I and Statement II are incorrect
   4. D.Statement I is incorrect but statement II is correct
   Show answer

   Answer: B

3. Q372023 · 13 Apr 2023 · Shift 2

   Two planets A and B of radii $\mathrm{R}$ and $1.5\mathrm{R}$ have densities $\rho$ and $\rho /2$ respectively. The ratio of acceleration due to gravity at the surface of B to A is:

   1. A.$2:1$
   2. B.$2:3$
   3. C.$4:3$
   4. D.$3:4$
   Show answer

   Answer: D

4. Q352023 · 12 Apr 2023 · Shift 1

   The ratio of escape velocity of a planet to the escape velocity of earth will be:- Given: Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.

   1. A.$1:4$
   2. B.$1:\sqrt{2}$
   3. C.$4:1$
   4. D.$2:1$
   Show answer

   Answer: D

5. Q362023 · 12 Apr 2023 · Shift 1

   Two satellites A and B move round the earth in the same orbit. The mass of A is twice the mass of B. The quantity which is same for the two satellites will be

   1. A.Potential energy
   2. B.Kinetic energy
   3. C.Total energy
   4. D.Speed
   Show answer

   Answer: D

6. Q352023 · 11 Apr 2023 · Shift 1

   The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are $\rho$ and $\rho /3$ respectively. The ratio of acceleration due to gravity at their surfaces ($g_A:g_B$) will be:

   1. A.$3:16$
   2. B.$4:3$
   3. C.$1:16$
   4. D.$3:4$
   Show answer

   Answer: D

7. Q442023 · 11 Apr 2023 · Shift 2

   A space ship of mass $2\times 10^4\text{ kg}$ is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if $g=10{\text{ m/s}}^2$ and radius of earth $=6400\text{ km}$):

   1. A.$7.9(\sqrt{2}-1)\text{km/s}$
   2. B.$11.2(\sqrt{2}-1)\text{km/s}$
   3. C.$7.4(\sqrt{2}-1)\text{km/s}$
   4. D.$8(\sqrt{2}-1)\text{km/s}$
   Show answer

   Answer: D

8. Q472023 · 11 Apr 2023 · Shift 2

   If $\mathrm{V}$ is the gravitational potential due to sphere of uniform density on its surface, then its value at the center of sphere will be:-

   1. A.$\frac{3}{2}\mathrm{V}$
   2. B.$\frac{\mathrm{V}}{2}$
   3. C.$\frac{4}{3}\mathrm{V}$
   4. D.$\mathrm{V}$
   Show answer

   Answer: A

9. Q502023 · 11 Apr 2023 · Shift 2

   In satellite communication, the uplink frequency band used is :

   1. A.$3.7-4.2\text{ GHz}$
   2. B.$5.925-6.425\text{ GHz}$
   3. C.$76-88\text{ MHz}$
   4. D.$420-890\text{ MHz}$
   Show answer

   Answer: B

10. Q422023 · 10 Apr 2023 · Shift 1

    Two satellites of masses m and 3m revolve around the earth in circular orbits of radii r & 3r respectively. The ratio of orbital speeds of the satellites respectively is

    1. A.$3:1$
    2. B.$\sqrt{3}:1$
    3. C.$1:1$
    4. D.$9:1$
    Show answer

    Answer: B

11. Q342023 · 8 Apr 2023 · Shift 1

    Given below are two statements: Statement I: If $\mathrm{E}$ be the total energy of a satellite moving around the earth, then its potential energy will be $\frac{\mathrm{E}}{2}$. Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy $\mathrm{E}$. In the light of the above statements, choose the most appropriate answer from the options given below

    1. A.Both Statement I and Statement II are incorrect
    2. B.Statement I is incorrect but Statement II is correct
    3. C.Statement I is correct but Statement II is incorrect
    4. D.Both Statement I and Statement II are correct
    Show answer

    Answer: A

12. Q372023 · 8 Apr 2023 · Shift 2

    The acceleration due to gravity at height $h$ above the earth if $h\ll \mathrm{R}$ (Radius of earth) is given by

    1. A.$g^{\prime }=g\left(1-\frac{2h}{R}\right)$
    2. B.$g^{\prime }=g\left(1-\frac{2h^2}{R^2}\right)$
    3. C.$g^{\prime }=g\left(1-\frac{h^2}{2R^2}\right)$
    4. D.$g^{\prime }=g\left(1-\frac{h}{2R}\right)$
    Show answer

    Answer: A

13. Q382023 · 6 Apr 2023 · Shift 1

    Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Earth has atmosphere whereas moon doesn't have any atmosphere. Reason R : The escape velocity on moon is very small as compared to that on earth. In the light of the above statements, choose the correct answer from the options given below:

    1. A.A is false but R is true
    2. B.Both A and R are correct but R is NOT the correct explanation of A
    3. C.Both A and R are correct and R is the correct explanation of A
    4. D.A is true but R is false
    Show answer

    Answer: C

14. Q422023 · 6 Apr 2023 · Shift 1

    A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing W on earth will weigh on that planet:

    1. A.$2^{2/3}\text{ W}$
    2. B.W
    3. C.$2\text{ W}$
    4. D.$2^{1/3}\text{ W}$
    Show answer

    Answer: D

15. Q472023 · 6 Apr 2023 · Shift 2

    The weight of a body on the surface of the earth is $100\text{ N}$. The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is:

    1. A.$50\text{ N}$
    2. B.$64\text{ N}$
    3. C.$25\text{ N}$
    4. D.$100\text{ N}$
    Show answer

    Answer: B

16. Q372023 · 1 Feb 2023 · Shift 1

    If earth has a mass nine times and radius twice to that of a planet P. Then $\frac{v_e}{3}\sqrt{x}{\text{ ms}}^{-1}$ will be the minimum velocity required by a rocket to pull out of gravitational force of P, where $v_e$ is escape velocity on earth. The value of $x$ is

    1. A.1
    2. B.3
    3. C.2
    4. D.18
    Show answer

    Answer: C

17. Q452023 · 30 Jan 2023 · Shift 1

    If the gravitational field in the space is given as $\left(-\frac{K}{r^2}\right)$. Taking the reference point to be at $r=2\text{ cm}$ with gravitational potential $V=10\text{ J/kg}$. Find the gravitational potential at $r=3\text{ cm}$ in SI unit (Given, that $\mathrm{K}=6Jcm/kg$)

    1. A.9
    2. B.11
    3. C.10
    4. D.12
    Show answer

    Answer: B

18. Q312023 · 29 Jan 2023 · Shift 1

    Two particles of equal mass '$m$' move in a circle of radius '$r$' under the action of their mutual gravitational attraction. The speed of each particle will be :

    1. A.$\sqrt{\frac{Gm}{4r}}$
    2. B.$\sqrt{\frac{Gm}{2r}}$
    3. C.$\sqrt{\frac{Gm}{r}}$
    4. D.$\sqrt{\frac{4Gm}{r}}$
    Show answer

    Answer: A

19. Q422023 · 29 Jan 2023 · Shift 2

    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.

    1. A.12 hours
    2. B.3 hours
    3. C.6 hours
    4. D.4 hours
    Show answer

    Answer: B

20. Q432023 · 24 Jan 2023 · Shift 2

    If the distance of the earth from Sun is $1.5\times 10^6\mathrm{km}$. Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is :

    1. A.$6\times 10^6\mathrm{km}$
    2. B.$3\times 10^7\mathrm{km}$
    3. C.$6\times 10^7\mathrm{km}$
    4. D.$3\times 10^6\mathrm{km}$
    Show answer

    Answer: D

21. Q502023 · 24 Jan 2023 · Shift 2

    Match List I with List II List-I: A. AM Broadcast B. FM Broadcast C. Television D. Satellite Communication List-II: I. 88-108 MHz II. 540-1600 kHz III. 3.7-4.2 GHz IV. 54MHz - 890MHz Choose the correct answer from the options given below :

    1. A.A-IV, B-III, C-I, D-II
    2. B.A-II, B-I, C-IV, D-III
    3. C.A-I, B-III, C-II, D-IV
    4. D.A-II, B-III, C-I, D-IV
    Show answer

    Answer: B