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Consider the following sketch of potenti...

Consider the following sketch of potential energy for a particle as a function of position. There are no dissipative forces or internal sources of energy.

What is the minimum total mechanical energy that the particle can have if you know that it has travelled over the entire region of `X` shown?

A

`-8`

B

`6`

C

`10`

D

It depends on direction of travel

Text Solution

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The correct Answer is:
C
If particle can reach point '`d`', then it can travel over the entire region.
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Two stars bound together by gravity orbit othe because of their mutual attraction. Such a pair of stars is referred to as a binary star system. One type of binary system is that of a black hole and a companion star. The black hole is a star that has cullapsed on itself and is so missive that not even light rays can escape its gravitational pull therefore when describing the relative motion of a black hole and 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=-GmM//r where G is the universal gravitational constant, m is the mass of the companion star, M is the mass of the black hole, and r is the distance between the centre of the companion star and the centre of the black hole. Since the gravitational force is conservative. The companion star and the centre of the black hole, since the gravitational force is conservative the companion star's total mechanical energy is a constant. Because of the periodic nature of of orbit there is a simple relation between the average kinetic energy ltKgt of the companion star Two special points along the orbit are single out by astronomers. Parigee isthe point at which the companion star is closest to the black hole, and apogee is the point at which is the farthest from the black hole. Q. For circular orbits the potential energy of the companion star is constant throughout the orbit. if the radius of the orbit doubles, what is the new value of the velocity of the companion star?

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