JEE Gravitation PYQs with Solutions PDF, Download Now

Initially a satellite of 100 kg is in a circular orbit of radius $$1.5R_{E}$$ This satellite can be moved to a circular orbit of radius $$3R_{E}$$ by supplying $$\alpha\times10^{6}J$$ of energy The value of $$\alpha$$ is ____. (Take Radius of Earth $$R_{E}=6\times10^{6}m\text{ and }g=10m/s^{2}$$)

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 $$T= 2\pi \sqrt{\frac{R_{e}}{g}}$$ (for satellite very close to the earth surface), where $$R_{e}$$ radius of earth and g acceleration due to gravity. In the light of the above statements , choose the correct answer from the options given below:

Net gravitational force at the center 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 $$\frac{F_{1}}{F_{2}}$$ is $$\frac{\alpha}{\sqrt{5}}$$ The value of $$\alpha$$ is _________.

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 ______$$m/s.$$

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet. Reason (R): The mass of the pendulum remains unchanged at Earth and the other planet. In the light of the above statements, choose the correct answer from the options given below :

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 $$F_1$$. A spherical part of radius R/3 is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be $$F_2$$ . The value of ratio $$F_1 : F_2$$ is

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 $$M\sqrt{\frac{GMR}{x}}$$.The value of $$x$$ is ______ , where M and R are the mass and radius of earth, respectively. ( G is the gravitational constant)

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

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 $$\underline{\hspace{2cm}}\,g.$$

A positive ion A and a negative ion B has charges $$6.67\times10^{-19}C$$ and $$9.6\times10^{-10}C$$, and masses $$19.2\times10^{-27}Kg$$ and $$9\times10^{-27}Kg$$ respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is $$P\times10^{45}$$ , where the value of 10P is (Take $$\frac{1}{4\pi\epsilon_{0}}=9\times10^{9}NM^{2}C^{-1}$$ and universal gravitational constant as $$6.67\times10^{-11}NM^{2}Kg^{-2}$$)
Assume that charge may not be an integral multiple of electrons.

Three equal masses m are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At t=0, they are given an initial velocity $$\vec{V}_A = V_0 \overrightarrow{AC}$$, $$\vec{V}_B = V_0 \overrightarrow{BA}$$ and $$\vec{V}_C = V_0 \overrightarrow{CB}$$. Here $$\overrightarrow{AC}$$, $$\overrightarrow{CB}$$ and $$\overrightarrow{BA}$$ are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is :

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 $$(L_{B})$$ of planet B to that of planet $$A(L_{A})$$ is closest to integer ________.

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:

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

If $$R$$ is the radius of the earth and the acceleration due to gravity on the surface of earth is $$g = \pi^2$$ m s$$^{-2}$$, then the length of the second's pendulum at a height $$h = 2R$$ from the surface of earth will be:

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 $$R^{-3/2}$$ then choose the correct option:

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 :

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 less time to move around the earth than the time taken by the earth to move around the sun.
In the light of the above statements, choose the most appropriate answer from the options given below :

At what distance above and below the surface of the earth a body will have same weight? (Take radius of earth as $$R$$)

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 gravitational potential at a point above the surface of earth is $$-5.12 \times 10^7 \text{ J kg}^{-1}$$ 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:

Escape velocity of a body from earth is 11.2 km s$$^{-1}$$. 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 planet is:

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

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

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

Correct formula for height of a satellite from earth's surface 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)

If $$G$$ be the gravitational constant and $$u$$ be the energy density then which of the following quantity have the dimensions as that of the $$\sqrt{uG}$$ :

A simple pendulum doing small oscillations at a place R height above earth surface has time period of $$T_1 = 4 \text{ s}$$. $$T_2$$ would be its time period if it is brought to a point which is at a height $$2R$$ from earth surface. Choose the correct relation $$[R = \text{radius of earth}]$$ :