## Numerical

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Two satellites resolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutio...
JEE Main 2021 (Online) 1st September Evening Shift
A body of mass (2M) splits into four masses (m, M $$-$$ m, m, M $$-$$ m}, which are rearranged to form a square as shown...
JEE Main 2021 (Online) 27th August Morning Shift
Suppose two planets (spherical in shape) in radii R and 2R, but mass M and 9M respectively have a centre to centre separ...
JEE Main 2021 (Online) 27th July Morning Shift
The radius in kilometer to which the present radius of earth (R = 6400 km) to be compressed so that the escape velocity ...
JEE Main 2021 (Online) 17th March Morning Shift
If one wants to remove all the mass of the earth to infinity in order to break it up completely.The amount of energy tha...
JEE Main 2021 (Online) 16th March Evening Shift
In the reported figure of earth, the value of acceleration due to gravity is same at point A and C but it is smaller tha...
JEE Main 2021 (Online) 26th February Evening Shift
The initial velocity vi required to project a body vertically upward from the surface of the earth to reach a height of ...
JEE Main 2021 (Online) 25th February Evening Shift
An asteroid is moving directly towards the centre of the earth. When at a distance of 10R (R is the radius of the earth)...
JEE Main 2020 (Online) 8th January Evening Slot

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Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction...
JEE Main 2021 (Online) 1st September Evening Shift
If RE be the radius of Earth, then the ratio between the acceleration due to gravity at a depth 'r' below and a height '...
JEE Main 2021 (Online) 31st August Evening Shift
The masses and radii of the earth and moon are (M1, R1) and (M2, R2) respectively. Their centres are at a distance 'r' a...
JEE Main 2021 (Online) 31st August Morning Shift
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 gravitationa...
JEE Main 2021 (Online) 27th August Evening Shift
Inside a uniform spherical shell :(1) the gravitational field is zero(2) the gravitational potential is zero(3) the grav...
JEE Main 2021 (Online) 26th August Morning Shift
The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 $$\times$$ 1...
JEE Main 2021 (Online) 27th July Evening Shift
Two identical particles of mass 1 kg each go round a circle of radius R, under the action of their mutual gravitational ...
JEE Main 2021 (Online) 27th July Evening Shift
Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average densit...
JEE Main 2021 (Online) 25th July Evening Shift
The minimum and maximum distances of a planet revolving around the sun are x1 and x2. If the minimum speed of the planet...
JEE Main 2021 (Online) 25th July Morning Shift
A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infini...
JEE Main 2021 (Online) 22th July Evening Shift
A satellite is launched into a circular orbit of radius R around earth, while a second satellite is launched into a circ...
JEE Main 2021 (Online) 20th July Evening Shift
A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acce...
JEE Main 2021 (Online) 20th July Morning Shift
The angular momentum of a planet of mass M moving around the sun in an elliptical orbit is $${\overrightarrow L }$$. The...
JEE Main 2021 (Online) 18th March Evening Shift
If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of...
JEE Main 2021 (Online) 18th March Evening Shift
The time period of a satellite in a circular orbit of radius R is T. The period of another satellite in a circular orbit...
JEE Main 2021 (Online) 18th March Morning Shift
Match List - I with List - II.List - I(a) 10 km height over earth's surface(b) 70 km height over earth's surface(c) 180 ...
JEE Main 2021 (Online) 18th March Morning Shift
A geostationary satellite is orbiting around an arbitrary planet 'P' at a height of 11R above the surface of 'P', R bein...
JEE Main 2021 (Online) 17th March Evening Shift
Two identical antennas mounted on identical towers are separated from each other by a distance of 45 km. What should nea...
JEE Main 2021 (Online) 16th March Evening Shift
Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the r...
JEE Main 2021 (Online) 26th February Morning Shift
A planet revolving in elliptical orbit has :A. a constant velocity of revolution.B. has the least velocity when it is ne...
JEE Main 2021 (Online) 26th February Morning Shift
Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2) from the earth's centre, where...
JEE Main 2021 (Online) 26th February Morning Shift
Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.Assertion A : The ...
JEE Main 2021 (Online) 25th February Morning Slot
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 respect...
JEE Main 2021 (Online) 25th February Morning Slot
A solid sphere of radius R gravitationally attracts a particle placed at 3R from its centre with a force F1. Now a spher...
JEE Main 2021 (Online) 25th February Morning Slot
A body weights 49N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine,...
JEE Main 2021 (Online) 24th February Evening Slot
Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revol...
JEE Main 2021 (Online) 24th February Morning Slot
Consider two satellites S1 and S2 with periods of revolution 1 hr. and 8 hr. respectively revolving around a planet in c...
JEE Main 2021 (Online) 24th February Morning Slot
Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the a...
JEE Main 2021 (Online) 24th February Morning Slot
Two planets have masses M and 16 M and their radii are $$a$$ and 2$$a$$, respectively. The separation between the centre...
JEE Main 2020 (Online) 6th September Evening Slot
The acceleration due to gravity on the earth’s surface at the poles is g and angular velocity of the earth about the axi...
JEE Main 2020 (Online) 5th September Evening Slot
The value of the acceleration due to gravity is g1 at a height h = $${R \over 2}$$ (R = radius of the earth) from the su...
JEE Main 2020 (Online) 5th September Morning Slot
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 ...
JEE Main 2020 (Online) 4th September Evening Slot
On the x-axis and at a distance x from the origin, the gravitational field due a mass distribution is given by $${{Ax} \... JEE Main 2020 (Online) 4th September Morning Slot The mass density of a planet of radius R varies with the distance r from its centre as$$\rho $$(r) =$${\rho _0}\left( ...
JEE Main 2020 (Online) 3rd September Evening Slot
A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth’...
JEE Main 2020 (Online) 3rd September Morning Slot
The height ‘h’ at which the weight of a body will be the same as that at the same depth ‘h’ from the surface of the eart...
JEE Main 2020 (Online) 2nd September Evening Slot
The mass density of a spherical galaxy varies as $${K \over r}$$ over a large distance ‘r’ from its centre. In that regi...
JEE Main 2020 (Online) 2nd September Morning Slot
Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities f...
JEE Main 2020 (Online) 9th January Evening Slot
A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass $${m \over 2}$$ coll...
JEE Main 2020 (Online) 9th January Morning Slot
Consider two solid spheres of radii R1 = 1m, R2 = 2m and masses M1 and M2, respectively. The gravitational field due to ...
JEE Main 2020 (Online) 8th January Morning Slot
A box weight 196 N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to th...
JEE Main 2020 (Online) 7th January Evening Slot
A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it rea...
JEE Main 2020 (Online) 7th January Morning Slot
The ratio of the weights of a body on the Earth’s surface to that on the surface of a planets is 9 : 4. The mass of the ...
JEE Main 2019 (Online) 12th April Evening Slot
A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the ...
JEE Main 2019 (Online) 10th April Evening Slot
The value of acceleration due to gravity at Earth's surface is 9.8 ms–2. The altitude above its surface at which the acc...
JEE Main 2019 (Online) 10th April Morning Slot
A test particle is moving in a circular orbit in the gravitational field produced by a mass density $$\rho (r) = {K \ove... JEE Main 2019 (Online) 9th April Evening Slot A solid sphere of mass 'M' and radius 'a' is surrounded by a uniform concentric spherical shell of thickness 2a and mass... JEE Main 2019 (Online) 9th April Morning Slot A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the ... JEE Main 2019 (Online) 8th April Evening Slot Four identical particles of mass M are located at the corners of a square of side 'a'. What should be their speed if eac... JEE Main 2019 (Online) 8th April Morning Slot Two satellites, A and B, have masses m and 2m respectively. A is in a circular orbit of radius R, and B is in a circular... JEE Main 2019 (Online) 12th January Evening Slot A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, fa... JEE Main 2019 (Online) 12th January Morning Slot A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass 'm' at x =... JEE Main 2019 (Online) 12th January Morning Slot The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of ... JEE Main 2019 (Online) 11th January Evening Slot A satellite is revolving in a circular orbit at a height h form the earth surface, such that h &lt; &lt; R where R is th... JEE Main 2019 (Online) 11th January Morning Slot Two stars of masses 3$$ \times $$1031 kg each, and at distance 2$$ \times $$1011 m rotate in a plane about their com... JEE Main 2019 (Online) 10th January Evening Slot A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from ... JEE Main 2019 (Online) 10th January Morning Slot The energy required to take a satellite to a height 'h' above Earth surface (radius of Earth = 6.4$$ \times $$103 km) ... JEE Main 2019 (Online) 9th January Evening Slot Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence : JEE Main 2018 (Online) 16th April Morning Slot Take the mean distance of the moon and the sun from the earth to be$$0.4 \times {10^6}$$km and$$150 \times {10^6}$$k... JEE Main 2018 (Online) 15th April Morning Slot A body of mass m is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two... JEE Main 2018 (Online) 15th April Morning Slot A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to t... JEE Main 2018 (Offline) A particle is moving in a circular path of radius$$a$$under the action of an attractive potential$$U = - {k \over {2...
JEE Main 2018 (Offline)
The mass density of a spherical body is given by $$\rho$$ (r) = $${k \over r}$$ for r $$\le$$ R and $$\rho$$ (r) = ...
JEE Main 2017 (Online) 9th April Morning Slot
If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the ea...
JEE Main 2017 (Online) 8th April Morning Slot
The variation of acceleration due to gravity $$g$$ with distance d from centre of the earth is best represented by (R = ...
JEE Main 2017 (Offline)
An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth’s surface. The radius...
JEE Main 2016 (Online) 10th April Morning Slot
Figure shows elliptical path abcd of a planet around the sun S such that the area of triangle csa is $${1 \over 4}$$ the...
JEE Main 2016 (Online) 9th April Morning Slot
A satellite is revolving in a circular orbit at a height $$'h'$$ from the earth's surface (radius of earth $$R;h &lt; ... JEE Main 2016 (Offline) From a solid sphere of mass$$M$$and radius$$R,$$a spherical portion of radius$$R/2$$is removed, as shown in the fi... JEE Main 2015 (Offline) Four particles, each of mass$$M$$and equidistant from each other, move along a circle of radius$$R$$under the action... JEE Main 2014 (Offline) What is the minimum energy required to launch a satellite of mass$$m$$from the surface of a planet of mass$$M$$and r... JEE Main 2013 (Offline) The mass of a spaceship is$$1000kg.$$It is to be launched from the earth's surface out into free space. The value... AIEEE 2012 Two cars of masses m1 and m2 are moving in circles of radii r1 and r2, respectively. Their speeds are such that they mak... AIEEE 2012 Two bodies of masses$$m$$and$$4m$$are placed at a distance$$r.$$The gravitational potential at a point on the... AIEEE 2011 The height at which the acceleration due to gravity becomes$${g \over 9}$$(where$$g=$$the acceleration due to gravit... AIEEE 2009 This question contains Statement -$$1$$and Statement -$$2$$. of the four choices given after the statements, choose t... AIEEE 2008 A planet in a density solar system is$$10$$times more massive than the earth and its radius is$$10$$times smaller. G... AIEEE 2008 Average density of the earth AIEEE 2005 The change in the value of$$g$$at a height$$h$$above the surface of the earth is the same as at a depth$$d$$below ... AIEEE 2005 A particle of mass$$10g$$is kept on the surface of a uniform sphere of mass$$100kg$$and radius$$10cm...
AIEEE 2005
Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circu...
AIEEE 2004
The time period of an earth satellite in circular orbit is independent of
AIEEE 2004
If $$g$$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mas...
AIEEE 2004
A satellite of mass $$m$$ revolves around the earth of radius $$R$$ at a height $$x$$ from its surface. If $$g$$ is the ...
AIEEE 2004
Two spherical bodies of mass $$M$$ and $$5M$$ &amp; radii $$R$$ &amp; $$2R$$ respectively are released in free space wit...
AIEEE 2003
The escape velocity for a body projected vertically upwards from the surface of earth is $$11$$ $$km/s.$$ If the body is...
AIEEE 2003
The time period of satellite of earth is $$5$$ hours. If the separation between the earth and the satellite is increased...
AIEEE 2003
The escape velocity of a body depends upon mass as
AIEEE 2002
Energy required to move a body of mass $$m$$ from an orbit of radius $$2R$$ to $$3R$$ is
AIEEE 2002
The kinetic energy needed to project a body of mass $$m$$ from the earth surface (radius $$R$$) to infinity is
AIEEE 2002
If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then ...
AIEEE 2002