Suppose the gravitational portential due to a small system is `k/r^2` at distance r from it. What will be the gravitational fied? Can you think of any such system? What happens if there were negative masses?

A cavity of radius R//2 is made inside a solid sphere of radius R . The centre of the cavity is located at a distance R//2 from the centre of the sphere. The gravitational force on a particle of a mass 'm' at a distance R//2 from the centre of the sphere on the line joining both the centres of sphere and cavity is (opposite to the centre of cavity). [Here g=GM//R^(2) , where M is the mass of the solide sphere]

There is a concentric hole of radius R in a solid sphere of radius 2R. Mass of the remaining portional is M. What is the gravitational potential at centre?

In a certain region of space, the gravitational field is given by -(k)/(r) where r is the distance and k is a constant. If the gravitaional potential at r=r_(0) be V_(0) , then what is the expression for the gravitaional potential (V)-

A particle of mass M is placed at the centre of a spherical shell of same mass and radius a. What will be the magnitude of the gravitational potential at a point situated at a/2 distance from the centre ?

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?

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. Which of the following prevents the companion star from leaving its orbit and falling the black hole?

A thin spherical shell of total mass M and radius R is held fixed. There is a small hole in the shell. A mass m is released from rest a distance R from the hole along a line that passes through the hole and also through the centre of the shell. This mass subsequently moves under the gravitational force of the shell. How long does the mass take to travel from the hole to the point diametrically opposite.

Obtain an expression of acceleration produced by gravity of earth. OR Obtain general equation of gravitation force at distance r from the centre of earth and derive the equation of acceleration due to gravity on the surface of earth.

If the gravitational force between two objects were proportional to 1/R (and not as 1/R^2 ) where R is the distance between them, then a particle in a circular path (under such a force) would have its orbital speed v_1 proportional to .........

A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to F_(1) on a particle placed at P , distance 2R from the centre O of the sphere. A spherical cavity of radius R//2 is now made in the sphere as shown in figure. The particle with cavity now applies a gravitational force F_(2) on same particle placed at P . The radio F_(2)//F_(1) will be