A large fluid star oscillates in shape under the influence of its own gravitational field. Using dimensional analysis, find the expression for period of oscillation (T) in terms of radius of star (R ), mean density of fluid `(rho)` and universal gravitational constant (G).

The distance moved by a particle in time from centre of ring under the influence of its gravity is given by x=a sin omegat where a and omega are constants. If omega is found to depend on the radius of the ring (r), its mass (m) and universal gravitation constant (G), find using dimensional analysis an expression for omega in terms of r, m and G.

Although a photon has no rest mass, but it possesses the inertial mass m="hf"/c^2 where h is Planck's constant , f is frequency of light and c is speed of light . Since light is deflected by a gravitational field , so it is naturally assured that photons have same gravitational behaviour as other particles. When photon is emitted from source of star of mass M and radius R, total energy of photon will be sum of hf and gravitational potential energy. At a large distance from star, the photon is beyond the star's gravitational field , so its gravitational potential energy becomes zero but its total energy remains constant. So frequency of a photon emitted from surface of a star decreases as it moves away from star. A photon in visible region of spectrum is thus shifted towards red end, and this phenomena is known as gravitational red shift. The potential energy of photon which is at surface of star is (where , M=Mass of the star , R=Radius of the star, G=Universal gravitational constant )

Find the minimum radius for a planet of mean density rho and temperature T which can detain oxygen in its atmosphere. ( M_(0)= Molecular weight of Oxygen and G= Universal Gravitational constant)

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.

The time period T of the moon of planet mars (mass M_(m) ) is related to its orbital radius R as ( G =gravitational constant)