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 :

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.

The distance of two planets from the sun are 10^(13) and 10^(12) m respectively. The ratio of the periods of the planet is

Two planets of masses M and M/2 have radii R and R/2 respectively. If ratio of escape velocities from their surfaces (v_1)/(v_2) is n/4 , then find n :

Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9 M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'v' required for the satellite to reach the surface of the second planet is sqrt((a)/(7) (GM)/(R )) then the value of 'a' is ________. [Given : The two planets are fixed in their position]

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.

Two planets of mass M and 16M of radius a and 2a respectively, are at distance 10a . Find minimum speed of a particle of mass m at surface of smaller planet so that it can reached from smaller planet to larger planet.

Two planets A and B are at distances of 10^(9) m and 10^(11) m from the sun respectively. Calculate the ration of speeds of the two planets.

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 .