The distance between the centres of two stars is `10alpha`. The masses of these stars are M and 16M and their radii `alpha ` and `2alpha`. A body of mass m is fired straight from the surface of the larger star towards the smaller star. What should be its minimum initial speed to reach the surface of teh smaller star? Obtain the expression interms of G, M and `alpha`.

Distance between the centres of two stars is 10a . The masses of these stars are M and 16 M ans their radit a nd 2a respectively. A body of mass m is fired straight from the surface of the larger star tpwards the surface of the smaller star. What should be its minimum intial speed to reach the surface of the smaller star? Obtain the expression in terms of G , M and a.

Distance between the centres of two rings is a. The masses of these rings are M and 4M . A body of mass m is fired straight from the centre of the heavier ring. What should be its minimum initial speed to cross of lighter ring ? The radius of the both ring is R . (Assume a gt gt R ).

Two stars of masses M and 4M have radii x and 3x respectively. The distance between centres of two stars is 12x. A body of mass m is fired from the surface of bigger sphere towards smaller sphere. Find the minimum initial speed (in terms of G, x, M) required to reach the surface of smaller star.

Two planets have masses M and 16 M and their radii are a and 2a, respectively. The separation between the centres of the planets is 10a. A body of mass m is fired trom the surface of the larger planet towards the samller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is :

A body of mass m kg falling from a distance 3R above the earth's surface. What is its kinetic enrgy when it reaches a distance 'R' above the surface of the earth of radius R and mass M ?

A particle is projected from the surface of one star towards other star of same radius a and mass with such a minimum velocity Ksqrt((GM)/a) , so that it is attracted towards other star. Find the value of K if two stars are 2r distance apart:

A pair of stars rotates about their centre of mass One of the stars has a mass M and the other has mass m such that M =2m The distance between the centres of the stars is d (d being large compared to the size of either star) . The period of rotation of the stars about their common centre of mass (in time of d ,m ,G) is .

The masses of two stars are m_(1) and m_(2) , and their separation is l. Determine the period T of their revolution in circular orbits about a common centre.