Gravitation — JEE Main PYQs

Inside a uniform spherical shell :
(a) the gravitational field is zero
(b) the gravitational potential is zero
(c) the gravitational field is same everywhere
(d) the gravitation potential is same everywhere
(e) all the above

Choose the most appropriate answer from the options gi …

Consider two satellites ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ with periods of revolution 1 hr. and 8 hr. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite ${\mathrm{S}}_1$ to the angular velocity of satellites $S_2$ is:

Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be:

Two stars of masses $m$ and $2m$ at a distance $d$ rotate about their common centre of mass in free space. The period of revolution is:

A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other object in sky and take acceleration due to gravity on the surface of the Earth and mars as $10\mathrm{m}/{\mathrm{s}}^2$ and $4\mathrm{m}/{\mathrm{s}}^2$ respectively. Identify …

A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator?
[ use $\mathrm{g}=\frac{\mathrm{Gm}}{{\mathrm{R}}^2}=9.8{\mathrm{ms}}^{-2}$ and radius of earth, …

A satellite is launched into a circular orbit of radius R around earth, while a second satellite is launched into a circular orbit of radius 1.02 R. The percentage difference in the time periods of the two satellites is :

Consider a binary star system of star A and star B with masses $m_A$ and $m_B$ revolving in a circular orbit of radii $r_A$ and $r_B$, respectively. If $T_A$ and $T_B$ are the time period of star A and star B, respectively, then :

A mass of 50 kg is placed at the centre of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the centre is $\mathrm{V}\mathrm{kg}/\mathrm{m}$. The value of V is:

A solid sphere of radius R gravitationally attracts a particle placed at $3R$ from its centre with a force $F_1$. Now a spherical cavity of radius $\left(\frac{\mathrm{R}}{2}\right)$ is made in the sphere (as shown in figure) and the force becomes $F_2$. The value of …

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The escape velocities of planet $A$ and $B$ are same. But $A$ and $B$ are of unequal mass.
Reason R: The product of their mass and radius must be same. …

Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively.
If $T_A$ and $T_B$ are the time periods of $A$ and $B$ respectively then the value of $T_B-T_A$:
[ Given : radius of earth …

A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height $h$ is ______ s.

Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If $\sqrt{8}R$ is the distance between the centres of a ring (of mass ' $m$ ') and a sphere (mass ' M …

A planet revolving in elliptical orbit has :
(A) a constant velocity of revolution.
(B) has the least velocity when it is nearest to the sun.
(C) its areal velocity is directly proportional to its velocity.
(D) areal velocity is inversely proportional to its velocity.
(E) To foll …

A body of mass (2M) splits into four masses $\{m,M-m,m,M-m\}$, which are rearranged to form a square as shown in the figure. The ratio of $\frac{M}{m}$ for which, the gravitational potential energy of the system becomes maximum is $x:1$. The value of $x$ is ______

In the reported figure of earth, the value of acceleration due to gravity is same at point A and C but it is smaller than that of its value at point B (surface of the earth). The value of $OA:AB$ will be $x:y$. The value of $x$ is ____

If $R_E$ be the radius of Earth, then the ratio between the acceleration due to gravity at a depth '$r$' below and a height '$r$' above the earth surface is:

The masses and radii of the earth and moon are ( ${\mathrm{M}}_1,{\mathrm{R}}_1$ ) and ( ${\mathrm{M}}_2,{\mathrm{R}}_2$ ) respectively. Their centres are at a distance ' $r$ ' apart. Find the minimum escape velocity for a particle of mass ' $m$ ' to be projected from t …

Suppose two planets (spherical in shape) of radii $R$ and $2R$, but mass M and 9M respectively have a centre to centre separation 8R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second p …

The radius in kilometre to which the radius of earth $(\mathrm{R}=6400\mathrm{km})$ to be compressed so that the escape velocity is increased 10 times is ______ .

The minimum and maximum distances of a planet revolving around the Sun are $x_1$ and $x_2$. If the minimum speed of the planet on its trajectory is $v_0$ then its maximum speed will be :

Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be :

The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of $9.0\times 10^3\mathrm{km}$. Find the mass of Mars.
$\{$ Given $\frac{4{\pi }^2}{\mathrm{G}}=6\times 10^{11}{\mathrm{N}}^{-2}{\mathrm{kg}}^2\}$

Two identical particles of mass 1 kg each go round a circle of radius R , under the action of their mutual gravitational attraction. The angular speed of each particle is :

Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction as shown in figure. The speed of each particle is:

The satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hours respectively. The radius of the orbit of nearer satellite is $2\times 10^3\mathrm{km}$. The angular speed of the farther satellit …

The maximum and minimum distances of a comet from the Sun are $1.6\times 10^{12}\mathrm{m}$ and $8.0\times 10^{10}\mathrm{m}$ respectively. If the speed of the comet at the nearest point is $6\times 10^4{\mathrm{ms}}^{-1}$, the speed at the farthest point is:

If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs so be supplied will be $\frac{x}{5}\frac{G{M}^2}{R}$ where $x$ is ⋯----. (Round off to the Nearest Integer)
( $M$ is the mass of earth, $R$ is the ra …

A particle of mass m moves in a circular orbit under the central potential field, $V(r)=-\frac{C}{r}$, where C is a constant. The correct radius - velocity graph of the particle's motion is ;

The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is $\vec{L}$. The magnitude of the areal velocity of the planet is ;

If the angular velocity of earth's spin is increased such that the bodies at the equator start floating , the duration of the day would be approximately :
[Take $g=10{\mathrm{ms}}^{-2}$, the radius of earth, $R=6400\times 10^3\mathrm{m}$, Take $\pi =3.14$ ]

A geostationary satellite is orbiting around an arbitrary planet ' $P$ ' at a height of $11R$ above the surface of ' $P$ ', $R$ being the radius of ' $P$ '. The time period of another satellite in hours at a height of 2R from the surface of ' $P$ ' is ____ ' $P$ ' has the ti …

The time period of satellite in a circular orbit of radius $R$ is $T$. The period of another satellite in a circular orbit of radius 9 R is:

A box weighs 196 N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take $\mathrm{g}=10{\mathrm{ms}}^{-2}$ at the north pole and the radius of the earth $=6400\mathrm{km}$)

Consider two solid spheres of radii ${\mathrm{R}}_1=1\mathrm{m}$, ${\mathrm{R}}_2=2\mathrm{m}$ and masses ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of …

Planet $A$ has mass $M$ and radius $R$. Plant $B$ has half the mass and half the radius of Planet $A$. If the escape velocities from the planets $A$ and $B$ are $V_A$ and $V_B$, respectively, then $\frac{V_A}{V_B}=\frac{n}{4}$. The value of ' $n$ ' i …

The acceleration due to gravity on the earth's surface at the poles is g an and angular velocity of the earth about the axis passing through the pole is $\omega$. An object is weight at the equator and at a height $h$ above the poles by using a spring balance. If the weights are …

A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius ${\mathrm{R}}_{\mathrm{e}}$. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become …

The mass density of a planet of radius R varies with the distance r from its centre as $\rho (r)={\rho }_0\left(1-\frac{r^2}{R^2}\right)$. Then the gravitational field is maximum at:

Two planets have masses M and 16 M and their radii are a and 2a, respectively. The separation between the centres of the planets is 10a. A body of mass m is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body t …

The value of the acceleration due to gravity is $g_1$ at a height $h=\frac{R}{2}$ ( $R=$ radius of the earth) from the surface of the earth. It is again equal to $g_1$ at a depth d below the surface of the earth. The ratio $\left(\frac{d}{R}\right)$ equals:

A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and fa …

On the $x$-axis and at a distance $x$ from the origin, the gravitational field due to a mass distribution is given by $\frac{Ax}{{\left(x^2+a^2\right)}^{3/2}}$ in the $x$-direction. The magnitude of gravitational potential on the $x$-axis at a distance $x$, taking its value …

A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is:

Four identical particles of mass M are located at the corners of a square of side '$a$'. What should be their speed if each of them revolves under the influence of other's gravitational field in a circular orbit circumscribing the square?

A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon? Assume that …

A solid sphere of mass ' M ' and radius ' a ' is surrounded by a uniform concentric spherical shell of thickness 2 a and mass 2 M . The gravitational field at distance ' 3 a ' from the centre will be:

A satellite is moving with a constant speed $v$ in circular orbit around the earth. An object of mass '$m$' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is:

The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2s. The period of oscillation of the same pendulum on the planet would be: