Gravitation — JEE Main PYQs

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is ______ m/s.

Net gravitational force at the centre of a square is found to be $F_1$ when four particles having mass $M,2M,3M$ and $4M$ are placed at the four corners of the square as shown in figure and it is $F_2$ when the positions of $3M$ and $4M$ are interchanged. The ratio …

Given below are two statements:
Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.
Statement II: The time period of revolution of the satellite is …

Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process ______ J.
(Gravitational constant …

Initially a satellite of 100 kg is in a circular orbit of radius $1.5{\mathrm{R}}_{\mathrm{E}}$. This satellite can be moved to a circular orbit of radius $3{\mathrm{R}}_{\mathrm{E}}$ by supplying $\alpha \times 10^6\mathrm{J}$ of energy. The value of $\alpha$ is ______.
(Take …

If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy (k) on reaching the surface of earth. The values of v and k respectively are ____.
(Take radius of earth to be 6400 km and $\mathrm{g}=9.8\mathrm{m}/{\mathrm{s}}^2$)

The height in terms of radius of the earth $(R)$, at which the acceleration due to gravity becomes $\frac{\mathrm{g}}{9}$, where $g$ is acceleration due to gravity on earth's surface, is $\_\_\_\_$ .

When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface. The change in g is approximately $\alpha \%$. The value of $\alpha$ is ______.
(Take radius of the earth $=6400$ km.)

A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth ($R_e$). The increase in potential energy will be ______.
($g$ is acceleration due to gravity at the surface of earth)

A planet (${\mathrm{P}}_1$) is moving around the star of mass 2 M in the orbit of radius R. Another planet (${\mathrm{P}}_2$) is moving around another star of mass 4 M in a orbit of radius $2R$. Ratio of time periods of revolution of $P_2$ and $P_1$ is ____.

A small point of mass $m$ is placed at a distance $2R$ from the centre 'O' of a big uniform solid sphere of mass M and radius R. The gravitational force on 'm' due to M is ${\mathrm{F}}_1$. A spherical part of radius $\mathrm{R}/3$ is removed from the big sphere as shown in th …

If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon $=27$ days and gravitational attraction between the satellite and the moon is neglected.

A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $M\sqrt{\frac{\text{GMR}}{x}}$. The value of $x$ is $\_\_\_\_$, where M and $R$ are the mass and radius of ea …

Two planets, A and B are orbiting a common star in circular orbits of radii $R_A$ and $R_B$, respectively, with $R_B=2R_A$. The planet $B$ is $4\sqrt{2}$ times more massive than planet $A$. The ratio $\left(\frac{L_B}{L_A}\right)$ of angular momentum …

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 $\mathrm{km}/\mathrm{s}$, the escape velocity in km/s from the planet will be :

Acceleration due to gravity on the surface of earth is ' g '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ______ g.

A satellite is launched into a circular orbit of radius ' R ' around the earth. A second statellite is launched into an orbit of radius 1.03 R . The time period of revolution of the second satellite is larger than the first one approximately by :-

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is ______ $\times 10^{10}\mathrm{J}$.
(Mass of earth $=6\times 10^{24}\mathrm{kg}$, Radius of earth …

Three identical spheres of mass m , are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time $\mathrm{T}=4$ seconds. If the sides of the triangle are increased to length 2a and also t …

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : The kinetic energy needed to project a body of mass m from earth surface to infinity is $\frac{1}{2}mgR$, where $R$ is the radius of earth.
Reason R : The maximum …

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.
Reason (R) : For …

An object is kept at rest at a distance of 3 R above the earth's surface where $R$ is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is :
(Assume $\mathrm{M}=$ mass of earth, $\mathrm{G}=$ Universal gravitational consta …

Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth?

Correct formula for height of a satellite from earths surface is :

Applying the principle of homogeneity of dimensions, determine which one is correct. where T is time period, G is gravitational constant, $M$ is mass, $r$ is radius of orbit.

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

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 $m$ is placed at the centre of the arc. The gravitational force on the particle by the wire is:

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 orbit of planet is : (Given = Radius of geo-stationary orbit for earth is $4.2\times 10^4$ km)

Match list-I with list-II:

(Where a = radius of planet orbit, r = radius of planet, M = mass of Sun, m = mass of planet)
Choose the correct answer from the options given below:

To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is ${\mathrm{R}}_{\mathrm{E}},\mathrm{g}=$ acceleration due to gravity on the surface of earth) :

Two planets A and B having masses ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ move around the sun in circular orbits of $r_1$ and $r_2$ radii respectively. If angular momentum of A is L and that of B is $3L$, the ratio of time period $\left(\frac{T_A}{T_B}\right)$ …

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

An astronaut takes a ball of mass m from earth to space. He throws the ball into a circular orbit about earth at an altitude of 318.5 km. From earth's surface to the orbit, the change in total mechanical energy of the ball is $x\frac{G{M}_{e}m}{21R_e}$. The value of x is (t …

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

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.
Reason (R): The moon takes l …

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?

The acceleration due to gravity on the surface of earth is g . If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

At what distance above and below the surface of the earth a body will have same weight, (take radius of earth as R.)

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 $\left(\frac{2\sqrt{2}+1}{32}\right)\frac{{\mathrm{Gm}}^2}{{\mathrm{L}}^2}$, the length of the sides of the square is

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

Escape velocity of a body from earth is $11.2\mathrm{km}/\mathrm{s}$. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is:

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

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

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

The weight of a body on the earth is 400 N. Then weight of the body when taken to a depth half of the radius of the earth will be:

Given below are two statements:

Statement I:

If E be the total energy of a satellite moving around the earth, then its potential energy will be $\frac{E}{2}$.

Statement II:

The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total e …

Choose the incorrect statement from the following:

The weight of a body on the surface of the earth is 100 N. The gravitational force on it when taken at a height, from the surface of earth, equal to onefourth the radius of the earth is:

Given below are two statements:

Statement I: Rotation of the earth shows effect on the value of acceleration due to gravity (g).

Statement II: The effect of rotation of the earth on the value of ' $g$ ' at the equator is minimum and that at the pole is maximum.

In the light …

The time period of a satellite, revolving above earth's surface at a height equal to $R$ will be (Given $\mathrm{g}={\pi }^2\mathrm{m}/{\mathrm{s}}^2,\mathrm{R}=$ radius of earth)