A body of mass '$$\mathrm{m}$$' kg starts falling from a distance 3R above earth's surface. When it reaches a distance '$$R$$' above the surface of the earth of radius '$$R$$' and Mass '$$M$$', then its kinetic energy is

A body is projected vertically from earth's surface with velocity equal to half the escape velocity. The maximum height reached by the satellite is ( $$R$$ = radius of earth)

A system consists of three particles each of mass '$$m_1$$' placed at the corners of an equilateral triangle of side '$$\frac{\mathrm{L}}{3}$$', A particle of mass '$$\mathrm{m}_2$$' is placed at the mid point of any one side of the triangle. Due to the system of particles, the force acting on $$\mathrm{m}_2$$ is

A satellite moves in a stable circular orbit round the earth if (where $$\mathrm{V}_{\mathrm{H}}, \mathrm{V}_{\mathrm{c}}$$ and $$\mathrm{V}_{\mathrm{e}}$$ are the horizontal velocity, critical velocity and escape velocity respectively)