Bansal Classes Gravitation Study Material

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Q. 1

Two satellites move along a circular orbit in the same direction at a small distance from each other. A container has to be thrown from the first satellite onto the second one. When will the container reach the second satellite faster: ifits is thrown in the direction of motion of the first satellite or in the opposite

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direction? The velocity of the container with respect to the satelliteu is much less than that of the satellite v.

Q.2

Because the Earth bulges near the equator, the source ofthe Mississippi River (at about 50"N latitude), although high above sea level, is about 5 km closer to the centre of the Earth than is its mouth (at about 300N latitude). How can the river flow "uphill" as it flows south?

Q.3

Use -qualitative arguments to explain why the following four periods are equal (all are 84 mill, assuming a uniform Earth density) : time of revolution of a satellite just above the Earthls surface period of oscillation of mail in a tunnel through the Earth ,period of a simple pendulum having a length equal to the Earthls radius in a uniform field 9.8 mI S2 period of an infinite simple pendulum in the Earth's real gravitational field.

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Q.4

After Sputnik I was put into orbit, it was said that it would not return to Earth but would bum up in its descent. Considering the fact that it did not bum up in its ascent, how is this possible?

Q.5

An artificial satellite is in a circular orbit about the Earth. How will its orbit change if one of its rockets is momentarily fired. (a) towards earth, (b) away from the'Earth, (c) in a forward direction, (d) in a backward direction, and (e) at right angles to the plane of the orbit?

Q.6

A stone is dropped along the centre of a deep vertical mine shaft. Assume no air resistance but consider the Earthls rotation. WIll the stone continue along the centre of the shaft? If not, describe its motion,

Q.7

An iron cube is placed near an iron sphere at a location remote from the Earth's gravity. What can you say about the location of the centre of gravity ofthe cube? Dfthe sphere? In general, does the location ofthe centre of gravity ofan object depend on the nature of the gravitational field in which the object is ill /' placed? ,

Q.8

Figure shows a particle of mass m that is moved from an infinite distance to the

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centre of a ri~ of mass M,alo~g ~he central axis of the ~ing. For the tri?, how

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does the magnitude of the gr~Vltational force on the particle due to the rmg c1lange ..

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end in time(neglect earthorientation rotation) through earth, then a ball released .'. 73 / If a tunnel is cut at any from one end will reac,h th,e other (A) 84.6 minutes (B) 42.3 minutes (C) 8 minutes (D) depends on orientation

{I () 4JBansal Classes

Question Bank on Gravitation

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Questions 74 to 79 (6 questions) Two stars bound together by gravity orbit each other because of their mutual attraction. Such a pair of stars is referred to as a binary star system. One type ofbinary system is that of a black hole and a companion star, The black hole is a star that has collapsed on itself and is so massive that not even light rays can escape it~ gravitational pull. Therefore, when describing the relative motion of a black hole and a companion star, the motion of the black hole can be assumed negligible compared to that of the companion. The orbit of the companion star is either elliptical with the black hole at one of the foci or circular with the black hole at the centre. The gravitational potential energy is given by U = - GmMir, where G is the universal gravitational constant, m is the mass of the companion star, M is the mass of the black hole, ane r is the distance between the centre of the companion star and the centre of the black hole. Since th{ gravitational force is conservative, the companion star's total mechanical energy is a constant oftht motion. Because of the periodic nature of the orbit, there is a simple relation betweenthe average kinetic energy ofthe companion star and its average potential energy < U>. In particular, = -