The gravitational potential energy of an isolated system of three particles, each of mass \(\mathrm{m}\) placed at three corners of an equilateral triangle of side \(\mathrm{l}\) is: 

An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy ${\mathrm{E}}_0$ . Its potential energy is?         

1. $-{\mathrm{E}}_0$                       

2. $1.5$ ${\mathrm{E}}_0$

3. $2{\mathrm{E}}_0$                         

4. ${\mathrm{E}}_0$

A satellite of mass \(m\) is orbiting the earth (of radius \(R\)) at a height \(h\) from its surface. What is the total energy of the satellite in terms of \(g_0?\)
(\(g_0\) is the value of acceleration due to gravity at the earth's surface)
1. \(\frac{mg_0R^2}{2(R+h)}\)
2. \(-\frac{mg_0R^2}{2(R+h)}\)
3. \(\frac{2mg_0R^2}{(R+h)}\)
4. \(-\frac{2mg_0R^2}{(R+h)}\)

A body of mass \(m\) is taken from the Earth’s surface to the height equal to twice the radius \((R)\) of the Earth. The change in potential energy of the body will be: 

The energy required to move a satellite of mass m from an orbit of radius 2R to 3R around the Earth having mass M is:

A body of mass m is situated at a distance 4${\mathrm{R}}_{\mathrm{e}}$ above the Earth's surface, where ${\mathrm{R}}_{\mathrm{e}}$ is the radius of the Earth. What minimum energy should be given to the body so that it may escape? 

The change in the potential energy, when a body of mass m is raised to a height nR from the

Earth's surface is: (R = Radius of the Earth)

1. $mgR\left(\frac{n}{n-1}\right)$                     

2. nmgR

3. mgR$\left(\frac{n^2}{n^2+1}\right)$                   

4. $mgR\left(\frac{n}{n+1}\right)$

Three equal masses \(\text{(m)}\) are placed at the three vertices of an equilateral triangle of side \(\text{r}\). Work required to double the separation between masses will be:-

A satellite of mass 1000 kg revolves in a circular orbit around the earth with a constant speed of 100 m/ s. The total mechanical energy of the satellite is:

If a particle is dropped from a height h = 3 R from the earth's surface, the speed with which the particle will strike the ground is :

1.  $\sqrt{3 \mathrm{gR}}$

2.  $\sqrt{2 \mathrm{gR}}$

3.  $\sqrt{1.5 \mathrm{gR}}$

4.  $\sqrt{\mathrm{gR}}$