Binary stars of comparable masses `m_(1)` and `m_(2)` rotate under the influence of each other's gravity with a time period `T`. If they are stopped suddenly in their motions, find their relative velocity when they collide with each constant of gravitation.

Binary stars of comparable masses rotates under the influence of each other's gravity at a distance [(2G)/(omega^(2))]^(1//3) where omega is the angular velocity of each of the system. If difference between the masses of two stars is 6 units. Find the ratio of the masses of smaller to bigger star.

Two particles of mass m_(1) and m_(2) , approach each other due to their mutual gravitational attraction only. Then

Two particles of mass m_(1) and m_(2) , approach each other due to their mutual gravitational attraction only. Then

Two bodies of masses m_1 and m_2 initially at rest at infinite distance apart move towards each other under gravitational force of attraction. Their relative velocity of approach when they are separated by a distance r is (G= universal gravitational constant.)

Two particles of masses m_(1) and m_(2) initially at rest a infinite distance from each other, move under the action of mutual gravitational pull. Show that at any instant therir relative velocity of approach is sqrt(2G(m_(1)+m_(2))//R) where R is their separation at that instant.

A uniform rod AB of mass m length 2a is allowed to fall under gravity with AB in horizontal. When the speed of the rod is v suddenly the end A is fixed. Find the angular velocity with which it begins to rotate.

Two particles of mass m_(1) and m_(2) are approaching towards each other under their mutual gravitational field. If the speed of the particle is v, the speed of the center of mass of the system is equal to :