Previous Year Questions

Gravitation

- Practice Previous Year questions to get a better exam idea
1
JEE Mains
Planet has mass and radius . Planet has half the mass and half the radius of planet If the escape velocities from the planets and are and respectively, then
The value of is
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An asteroid is moving directly towards the centre of the earth. When at a distance of ( is the radius of the earth) from the earth centre, it has a speed of . Neglecting the effect of the earths atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is )? Give your answer to the nearest integer in kilometer/s _____
Consider two solid spheres of radii and masses and , respectively. The gravitational field due to sphere (1) and (2) are shown. The value of is:
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A box weights 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 at the north pole and the radius of the earth ):
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A satellite of mass is launched vertically upwards with an initial speed from the surface of the earth. After it reaches height R(R= radius of the earth), it ejects a rocket of mass so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is ( is the gravitational constant; is the mass of the earth) :
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The ratio of the weights of a body on the Earth's surface to that on the surface of a planet is . The mass of the planet is of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ?
(Take the planets to have the same mass density)
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A test particle is moving in a circular orbit in the gravitational field produced by a mass density . Identify the correct relation between the radius R of the particle's orbit and its period T.
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is a constant
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is a constant
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is a constant
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is a constant
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 the density of the earth and the moon are equal and that the earth's volume is 64 times the volume of the moon :
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Four identical particles of mass are located at the corners of a square of side . 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?
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The variation of acceleration due to gravity with distance from centre of the earth is best represented by (R=Earth's radius) :
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A satellite is revolving in a circular orbit at a height 'h' from the earth's surface(radius of earth R hR). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is closed to(Neglect the effect of atmosphere.)
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2
A planet of mass M, has two natural satellites with masses and . The radii of their circular orbits are and respectively. Ignore the gravitational force between the satellites. Define and to be respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite ; and and to be the corresponding quantities of satellite . Given and , match the ratios in List - I to the numbers in List-II.

 List - I List - II P. 1. Q. 2. R. 3. S. 4.

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A rocket is launched normal to the surface of the Earth, away from the Sun, along the line, joining the Sun and the Earth. The Sun is times heavier than the Earth and is at a distance times larger than the radius of the Earth. The escape velocity from Earth's gravitational field is . The minimum initial velocity required for the rocket to be able to leave the Sun-Earth system is closest to (Ignore the rotation and revolution of the Earth and the presence of any other planet)
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A bullet is fired vertically upwards with velocity from the surface of a spherical planet. When it reaches its maximum heights, its acceleration due to the planet's gravity is th of its value at the surface of the planet. If the escape velocity from the planet is , then the value of N is (ignore energy loss due to atmosphere)
A large spherical mass M is fixed at one position and two identical point masses m are kept on a line passing through the centre of M. The point masses are connected by a rigid massless rod of length and this assembly is free to move along the line connecting them. All three masses interact only through their mutual gravitational interaction. When the point mass nearer to M is at a distance from M, the tension in the rod is zero for . The value of k is
Two bodies, each of mass are kept fixed at a separation . A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is The correct statement(s) is (are)
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The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is
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The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is
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The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is
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The energy of the mass m remains constant.
A planet of radius has the same mass density as Earth. Scientists dig a well of depth on it and lower a wire of the same length and of linear mass density into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is (take the radius of Earth  and the acceleration due to gravity of Earth is 10)
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