Gravitation · JEE Main previous year questions

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.${\mathrm{T}}^2\propto {\mathrm{R}}^{3/2}$

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.$\frac{L}{2}$

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.$\frac{\mathrm{v}}{3}$

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.$1000\text{ km}$

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

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.$67.2$

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

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.$3:4$

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.$2:1$

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

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.$3:4$

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.$8(\sqrt{2}-1)\text{km/s}$

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.$\mathrm{V}$

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.$420-890\text{ MHz}$

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.$9:1$

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

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.$g^{\prime }=g\left(1-\frac{h}{2R}\right)$

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

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.$2^{1/3}\text{ W}$

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.$100\text{ N}$

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

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

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.$\sqrt{\frac{4Gm}{r}}$

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

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.$3\times 10^6\mathrm{km}$