Gravitation · JEE Main previous year questions

2024 11 questions

1. Q352024 · 9 Apr 2024 · Shift 2

   A satellite of $10^3\mathrm{kg}$ mass is revolving in circular orbit of radius $2R$. If $\frac{10^{4}R}{6}\mathrm{J}$ energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use $g=10m/{\mathrm{s}}^2$, $R=$ radius of earth)

   1. A.$4\mathrm{R}$
   2. B.$6\mathrm{R}$
   3. C.$2.5\mathrm{R}$
   4. D.$3\mathrm{R}$
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   Answer: B

2. Q352024 · 8 Apr 2024 · Shift 2

   Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of A is $3v$, the speed of B will be :

   1. A.$6v$
   2. B.$\frac{4}{3}v$
   3. C.$3v$
   4. D.$12v$
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   Answer: A

3. Q422024 · 5 Apr 2024 · Shift 2

   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 of orbit of the satellite is : (Given $=$ Radius of geo-stationary orbit for earth is $4.2\times 10^4\mathrm{km}$)

   1. A.$1.68\times 10^5\mathrm{km}$
   2. B.$1.4\times 10^4\mathrm{km}$
   3. C.$8.4\times 10^4\mathrm{km}$
   4. D.$1.05\times 10^4\mathrm{km}$
   Show answer

   Answer: D

4. Q332024 · 4 Apr 2024 · Shift 1

   A metal wire of uniform mass density having length $L$ and mass $M$ is bent to form a semicircular arc and a particle of mass $\mathrm{m}$ is placed at the centre of the arc. The gravitational force on the particle by the wire is :

   1. A.$\frac{\mathrm{GmM}{\pi }^2}{{\mathrm{L}}^2}$
   2. B.$\frac{\mathrm{GmM}\pi }{2{\mathrm{L}}^2}$
   3. C.0
   4. D.$\frac{2\mathrm{GmM}\pi }{{\mathrm{L}}^2}$
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   Answer: D

5. Q392024 · 4 Apr 2024 · Shift 2

   A $90\text{ kg}$ body placed at $2\text{R}$ distance from surface of earth experiences gravitational pull of : $(\text{R}=\text{Radius of earth},g=10{\text{ m s}}^{-2})$

   1. A.$300\text{ N}$
   2. B.$225\text{ N}$
   3. C.$100\text{ N}$
   4. D.$120\text{ N}$
   Show answer

   Answer: C

6. Q462024 · 4 Apr 2024 · Shift 2

   Correct formula for height of a satellite from earth's surface is :

   1. A.${\left(\frac{T^2{R}^{2}g}{4{\pi }^2}\right)}^{1/3}-R$
   2. B.${\left(\frac{T^2{R}^{2}g}{4\pi }\right)}^{1/2}-R$
   3. C.${\left(\frac{T^2{R}^{2}g}{4{\pi }^2}\right)}^{-1/3}+R$
   4. D.${\left(\frac{T^2{R}^2}{4{\pi }^{2}g}\right)}^{1/3}-R$
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   Answer: A

7. Q422024 · 1 Feb 2024 · Shift 2

   A light planet is revolving around a massive star in a circular orbit of radius $\mathrm{R}$ with a period of revolution $\mathrm{T}$. If the force of attraction between planet and star is proportional to ${\mathrm{R}}^{-3/2}$ then choose the correct option :

   1. A.${\mathrm{T}}^2\propto {\mathrm{R}}^{7/2}$
   2. B.${\mathrm{T}}^2\propto {\mathrm{R}}^3$
   3. C.${\mathrm{T}}^2\propto {\mathrm{R}}^{5/2}$
   4. D.${\mathrm{T}}^2\propto {\mathrm{R}}^{3/2}$
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   Answer: C

8. Q312024 · 31 Jan 2024 · Shift 1

   Four identical particles of mass $m$ are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is $\left(\frac{2\sqrt{2}+1}{32}\right)\frac{{\mathrm{Gm}}^2}{L^2}$, the length of the sides of the square is

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

9. Q492024 · 31 Jan 2024 · Shift 2

   The mass of the moon is $\frac{1}{144}$ times the mass of a planet and its diameter is $\frac{1}{16}$ times the diameter of a planet. If the escape velocity on the planet is $v$, the escape velocity on the moon will be :

   1. A.$\frac{\mathrm{v}}{4}$
   2. B.$\frac{\mathrm{v}}{6}$
   3. C.$\frac{\mathrm{v}}{12}$
   4. D.$\frac{\mathrm{v}}{3}$
   Show answer

   Answer: D

10. Q502024 · 30 Jan 2024 · Shift 1

    The gravitational potential at a point above the surface of earth is $-5.12\times 10^7\text{ J/kg}$ and the acceleration due to gravity at that point is $6.4{\text{ m/s}}^2$. Assume that the mean radius of earth to be $6400\text{ km}$. The height of this point above the earth's surface is :

    1. A.$1600\text{ km}$
    2. B.$1200\text{ km}$
    3. C.$540\text{ km}$
    4. D.$1000\text{ km}$
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    Answer: A

11. Q382024 · 29 Jan 2024 · Shift 2

    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 :

    1. A.20
    2. B.50
    3. C.100
    4. D.25
    Show answer

    Answer: D