The escape velocity of a body on a planet 'A' is 12 kms^$$-$$1. The escape velocity of the body on another planet 'B', whose density is four times and radius is half of the planet 'A', is :

Water falls from a 40 m high dam at the rate of 9 $$\times$$ 10⁴ kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100 W lamps, that can be lit, is :

(Take g = 10 ms^$$-$$2)

Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be :

Two planets A and B of equal mass are having their period of revolutions T_A and T_B such that T_A = 2T_B. These planets are revolving in the circular orbits of radii r_A and r_B respectively. Which out of the following would be the correct relationship of their orbits?