The escape velocity for a body projected vertically upwards from the surface of earth is $$11$$ $$km/s.$$ If the body is projected at an angle of $${45^ \circ }$$ with the vertical, the escape velocity will be

Two spherical bodies of mass $$M$$ and $$5M$$ & radii $$R$$ & $$2R$$ respectively are released in free space with initial separation between their centers equal to $$12R$$. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is

The kinetic energy needed to project a body of mass $$m$$ from the earth surface (radius $$R$$) to infinity is

If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will