A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth’s radius R_e . By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become $$\sqrt {{3 \over 2}} $$ times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R. Value of R is :

The height ‘h’ at which the weight of a body will be the same as that at the same depth ‘h’ from the surface of the earth is (Radius of the earth is R and effect of the rotation of the earth is neglected)

The mass density of a spherical galaxy varies as $${K \over r}$$ over a large distance ‘r’ from its centre. In that region, a small star is in a circular orbit of radius R. Then the period of revolution, T depends on R as :

Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are v_A and v_B, respectively, then $${{{v_A}} \over {{v_B}}} = {n \over 4}$$. The value of n is :