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)

There is a second's pendulum on the surface of earth. It is taken to the surface of planet whose mass and radius are twice that of earth. The period of oscillation of second's pendulum on the planet will be