Gravitation — JEE Main PYQs

Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth $\mathrm{d}=\frac{\mathrm{R}}{2}$ from the surface of earth, if its weight on the surface of earth is 200 N, will be:
(Given $\mathrm{R}=$ Radius of earth)

Two satellites of masses m and 3 m revolve around the earth in circular orbits of radii $r\&3r$ respectively. The ratio of orbital speeds of the satellites respectively is :

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 $({\mathrm{g}}_{\mathrm{A}}:{\mathrm{g}}_{\mathrm{B}})$ will be:

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:

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.

A planet having mass 9 Me and radius $4{\mathrm{R}}_{\mathrm{e}}$, where Me and Re are mass and radius of earth respectively, has escape velocity in $\mathrm{km}/\mathrm{s}$ given by: (Given escape velocity on earth
$V_e=11.2\times 10^3\mathrm{m}/\mathrm{s}$ )

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, …

Two planets A and B of radii R and 1.5 R have densities $\rho$ and $\rho /2$ respectively. The ratio of acceleration due to gravity at the surface of B to A is :

Two identical particles each of mass 'm' go round a circle of radius $a$ under the action of their mutual gravitational attraction. The angular speed of each particle will be :

A body is released from a height equal to the radius (R) of the earth. The velocity of the body when it strikes the surface of the earth will be :
(Given $g=$ acceleration due to gravity on the earth.)

A planet has double the mass of the earth. Its average density is equal to the that of the earth. An object weighing W on earth will weigh on that planet :

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 …

If V is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:-

A spaceship of mass $2\times 10^4\mathrm{kg}$ is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be (if $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$ an …

Given below are two statements:
Statement-I: Acceleration due to gravity is different at different places on the surface of earth.
Statement-II: Acceleration due to gravity increases as we go down below the earth's surface.
In the light of the above statements, choose the correct …

If earth has a mass nine times and radius twice to the of a planet P. Then $\frac{v_e}{3}\sqrt{x}{\mathrm{ms}}^{-1}$ 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

The weight of a body at the surface of earth is 18 N . The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth ${\mathrm{R}}_{\mathrm{e}}=6400\mathrm{km}$)

If the distance of the earth from Sun is $1.5\times 10^6$ km. Then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is:

Given below are two statements:

Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.

Statement II: Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's surface, if h=d.

In the light of above …

A body of mass is taken from earth surface to the height $h$ equal to twice the radius of earth $(R_e)$, the increase in potential energy will be : ( $g=$ acceleration due to gravity on the surface of Earth)

Every planet revolves around the sun in an elliptical orbit :

A. The force acting on a planet is inversely proportional to square of distance from sun.

B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun

C. The centripetal for …

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 :

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.

An object is allowed to fall from a height R above the earth, where R is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be :

If the gravitational field in the space is given as $\left(-\frac{K}{r^2}\right)$. Taking the reference point to be at $r=2$ cm with gravitational potential $V=10$ J/kg. Find the gravitational potential at $r=3$ cm in SI unit (Given, that $K=6$ J cm/kg)

At a certain depth "d" below surface of earth. value of acceleration due to gravity becomes four times that of its value at a height $3R$ above earth surface. Where R is Radius of earth (Take $R=6400$ km). The depth d is equal to

A body weight W, is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be:

The escape velocities of two planets A and B are in the ratio $1:2$. If the ratio of their radii respectively is $1:3$, then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be:

An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be
[If, $g=10{\mathrm{ms}}^{-2}$ and radius of earth $=6400\mathrm{km}$]

If the radius of earth shrinks by $2\%$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :

Assume there are two identical simple pendulum Clocks-1 is placed on the earth and Clock-2 is placed on a space station located at a height h above the earth surface. Clock-1 and Clock-2 operate at time periods 4 s and 6 s respectively. Then the value of h is (consider radius of …

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 :

Three identical particle A, B and C of mass 100 kg each are placed in a straight line with $\mathrm{AB}=\mathrm{BC}=13\mathrm{m}$. The gravitational force on a fourth particle P of the same mass is F, when placed at a distance 13 m from the particle B on the perpendicular bis …

A body is projected vertically upwards from the surface of earth with a velocity equal to one third of escape velocity. The maximum height attained by the body will be:
(Take radius of earth $=6400\mathrm{km}$ and $\mathrm{g}=10{\mathrm{ms}}^{-2}$)

A body of mass $m$ is projected with velocity $\lambda v_e$ in vertically upward direction from the surface of the earth into space. It is given that ${\mathrm{v}}_{\mathrm{e}}$ is escape velocity and $\lambda <1$. If air resistance is considered to the negligible, then th …

An object is taken to a height above the surface of earth at a distance $\frac{5}{4}R$ from the centre of the earth. Where radius of earth, $R=6400\mathrm{km}$. The percentage decrease in the weight of the object will be

The percentage decrease in the weight of a rocket, when taken to a height of 32 km above the surface of earth will, be :
(Radius of earth $=6400\mathrm{km}$)

Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be:

Four spheres each of mass m form a square of side d (as shown in figure). A fifth sphere of mass M is situated at the centre of square. The total gravitational potential energy of the system is :

The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be :

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

Assertion A : If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its mag …

The escape velocity of a body on a planet ' A ' is $12{\mathrm{kms}}^{-1}$. The escape velocity of the body on another planet ' B ', whose density is four times and radius is half of the planet ' A ', is :

The variation of acceleration due to gravity (g) with distance ( $r$ ) from the center of the earth is correctly represented by : (Given $\mathrm{R}=$ radius of earth)

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 ans …

If the acceleration due to gravity experienced by a point mass at a height 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 …

The approximate height from the surface of earth at which the weight of the body becomes $\frac{1}{3}$ of its weight on the surface of earth is : [Radius of earth $\mathrm{R}=6400\mathrm{km}$ and $\sqrt{3}=1.732$ ]

The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3 R will be :

Two satellites $S_1$ and $S_2$ are revolving in circular orbits around a planet with radius $R_1=3200\mathrm{km}$ and $R_2=800\mathrm{km}$ respectively. The ratio of speed of satellite $S_1$ to the speed of satellite $S_2$ in their respective orbits would be …

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 $\mathrm{g}=$ acceleration due to gravity at the surface of earth)

Two planets A and B of equal mass have periods of revolution T_A and T_B such that T_A = 2 T_B. They revolve in circular orbits of radii r_A and r_B respectively. Which of the following is the correct relationship of their orbits?