An object of mass m is raised from the surface of the earth to a height equal to the radius of the earth, that is, taken from a distance $R$ to $2R$ from the centre of the earth. What is the gain in its potential energy ?

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

Choose the correct alternative:

$(a)$ If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic/potential energy.

$(b)$ The energy required to launch an orbiting satellite out of earth’s gravitational influence is more/less than the energy required to project a stationary object at the same height (as the satellite) out of earth’s influence.

Four particles $A, B, C$ and $D$ each of mass $m$ are kept at the corners of a square of side $L$. Now the particle $D$ is taken to infinity by an external agent keeping the other particles fixed at their respective positions. The work done by the gravitational force acting on the particle $D$ during its movement is ……….

The gravitational potential energy of a body of mass $‘m’$ at the earth’s surface $ – mg{R_e}$. Its gravitational potential energy at a height ${R_e}$ from the earth’s surface will be (Here ${R_e}$ is the radius of the earth)