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Select the proper graph between the gravitational potential (vg) due to hollow sphere and distance (r) from its centre

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Important Questions on Gravitation

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Consider two solid spheres of radii R1=1 m,R2=2 m and masses M1 and M2, respectively. The gravitational field due to sphere 1 and 2 are shown. The value of M1M2 is:

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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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What is the minimum energy required to launch a satellite of mass m from the surface of the earth of mass M and radius R at an altitude 2R?
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The change in potential energy when a body of mass m is raised to a height nR from the earth's surface is (R=radius of earth),
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A planet is orbiting the sun in an elliptical orbit. Let U denote the potential energy and K denote the kinetic energy of the planet at an arbitrary point on the orbit. Choose the correct statement-
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Consider a spherical gaseous cloud of mass density ρr in free space where r is the radial distance from its center. The gaseous cloud is made of particles of equal mass m moving in circular orbits about the common center with the same kinetic energy K . The force acting on the particles is their mutual gravitational force. If ρr is constant in time, the particle number density nr=ρr/m is: [ G is universal gravitational constant]
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A uniform cable of mass M and length L is placed on a horizontal surface such that its 1nth part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be:
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A spherically symmetric gravitational system of particles has mass density ρ=ρ0 for rR0 for r>R where, ρ0 is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed v as a function of distance r(0<r<) from the centre of the system is represented by

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Two particles of identical mass are moving in circular orbits under a potential given by Vr=Kr-n, where K is a constant. If the radii of their orbits are r1, r2 and their speeds are v1, v2 respectively, then
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An object is propelled vertically to a maximum height of, 4R from the surface of a planet of radius, R and mass M. The speed of object when it returns to the surface of the planet is
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On the x-axis and at a distance x from the origin, the gravitational field due to a mass distribution is given by axx2+a23/2 in the x-direction. The magnitude of the gravitational potential on the x-axis at a distance x, taking its value to be zero at infinity is:
HARD

From a solid sphere of mass M and radius R, a spherical portion of radius R2 is removed as shown in the figure. Taking gravitational potential V=0 at r=, the potential at the centre of the cavity thus formed is (G=gravitational constant)

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HARD
The mass density of a planet of radius R varies with the distance r from its centre as ρ(r)=ρ01-r2R2, then the gravitational field is maximum at:
HARD
A satellite of massM  is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R ( R= radius of the earth), it ejects a rocket of mass M10 so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is ( G is the gravitational constant; Me is the mass of the earth):
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A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point situated at a2 distance from the centre, will be 
 
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A particle falls towards earth from infinity. Its velocity on reaching the earth would be:
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Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is
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The gravitational field in a region is given by g=5i^+12j^ N kg-1. The change in the gravitational potential energy of a particle of mass 2 kg when it is taken from the origin to a point 7 m,-3 m is
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Which of the following most closely depicts the correct variation of the gravitation potential, V(r) with distance r due to a large planet of radius R and uniform mass density? (figures are not drawn to scale)
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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 equal masses. The first mass moves in a circular orbit of radius R2 . And the other mass, in a circular orbit of radius 3R2. The difference between the final and the initial total energies is