Gravitation · JEE Main previous year questions

2022 11 questions

1. Q522022 · 29 Jul 2022 · Shift 1· Numerical answer

   If the acceleration due to gravity experienced by a point mass at a height $\mathrm{h}$ above the surface of earth is same as that of the acceleration due to gravity at a depth $\alpha \mathrm{h}(\mathrm{h}\ll {\mathrm{R}}_{\mathrm{e}})$ from the earth surface. The value of $\alpha$ will be ____. (use ${\mathrm{R}}_{\mathrm{e}}=6400\mathrm{km}$)

   Show answer

   Answer: 2

2. Q342022 · 28 Jul 2022 · Shift 1

   A balloon has mass of $10\text{ g}$ in air. The air escapes from the balloon at a uniform rate with velocity $4.5\text{ cm/s}$. If the balloon shrinks in $5\text{ s}$ completely. Then, the average force acting on that balloon will be (in dyne).

   1. A.3
   2. B.9
   3. C.12
   4. D.18
   Show answer

   Answer: B

3. Q372022 · 28 Jul 2022 · Shift 2
   
   1. A.$11.6\text{ m/s}$
   2. B.$10.8\text{ m/s}$
   3. C.$17.8\text{ m/s}$
   4. D.$14.4\text{ m/s}$
   Show answer

   Answer: C

4. Q362022 · 27 Jul 2022 · Shift 1

   Two satellites A and B, having masses in the ratio $4:3$, are revolving in circular orbits of radii $3r$ and $4r$ respectively around the earth. The ratio of total mechanical energy of A to B is :

   1. A.$9:16$
   2. B.$16:9$
   3. C.$1:1$
   4. D.$4:3$
   Show answer

   Answer: B

5. Q362022 · 27 Jul 2022 · Shift 2

   A body of mass $\mathrm{m}$ is projected with velocity $\lambda v_e$ in vertically upward direction from the surface of the earth into space. It is given that $v_e$ is escape velocity and $\lambda <1$. If air resistance is considered to be negligible, then the maximum height from the centre of earth, to which the body can go, will be : ($\mathrm{R}$ : radius of earth)

   1. A.$\frac{\mathrm{R}}{1+{\lambda }^2}$
   2. B.$\frac{\mathrm{R}}{1-{\lambda }^2}$
   3. C.$\frac{\mathrm{R}}{1-\lambda }$
   4. D.$\frac{{\lambda }^2\mathrm{R}}{1-{\lambda }^2}$
   Show answer

   Answer: B

6. Q332022 · 30 Jun 2022 · Shift 1

   The radii of two planets A and B are in the ratio $2:3$. Their densities are $3\rho$ and $5\rho$ respectively. The ratio of their acceleration due to gravity is :

   1. A.$9:4$
   2. B.$9:8$
   3. C.$9:10$
   4. D.$2:5$
   Show answer

   Answer: D

7. Q352022 · 28 Jun 2022 · Shift 2

   Water falls from a $40\text{ m}$ high dam at the rate of $9\times 10^4\text{ kg}$ per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of $100\text{ W}$ lamps, that can be lit, is : (Take $g=10{\text{ ms}}^{-2}$)

   1. A.$25$
   2. B.$50$
   3. C.$100$
   4. D.$18$
   Show answer

   Answer: B

8. Q372022 · 27 Jun 2022 · Shift 1

   Given below are two statements : Statement I : The law of gravitation holds good for any pair of bodies in the universe. Statement II : The weight of any person becomes zero when the person is at the centre of the earth. In the light of the above statements, choose the correct answer from the options given below.

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

   Answer: A

9. Q362022 · 27 Jun 2022 · Shift 2
   
   1. A.$-\frac{Gm}{d}\left[(4+\sqrt{2})m+4\sqrt{2}M\right]$
   2. B.$-\frac{Gm}{d}\left[(4+\sqrt{2})M+4\sqrt{2}m\right]$
   3. C.$-\frac{Gm}{d}\left[3m^2+4\sqrt{2}M\right]$
   4. D.$-\frac{Gm}{d}\left[6m^2+4\sqrt{2}M\right]$
   Show answer

   Answer: A

10. Q352022 · 25 Jun 2022 · Shift 1

    The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be : (Given g = acceleration due to gravity at the surface of earth).

    1. A.g/2
    2. B.g/4
    3. C.g/3
    4. D.g/9
    Show answer

    Answer: D

11. Q552022 · 25 Jun 2022 · Shift 2· Numerical answer

    Two satellites ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ are revolving in circular orbits around a planet with radius ${\mathrm{R}}_1=3200\mathrm{km}$ and ${\mathrm{R}}_2=800\mathrm{km}$ respectively. The ratio of speed of satellite ${\mathrm{S}}_1$ to be speed of satellite ${\mathrm{S}}_2$ in their respective orbits would be $\frac{1}{x}$ where $x=\underline{}$.

    Show answer

    Answer: 2