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 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? 

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:-

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.  $\sqrt{\mathrm{gR}}$

A rocket of mass M is launched vertically from the surface of the earth with an initial speed v. Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is   

1. $\mathrm{R}/\left(\frac{\mathrm{gR}}{2{\mathrm{v}}^2}-1\right)$                         

2. $\mathrm{R}\left(\frac{\mathrm{gR}}{2{\mathrm{v}}^2}-1\right)$

3. $\mathrm{R}/\left(\frac{2\mathrm{gR}}{{\mathrm{v}}^2}-1\right)$                         

4. $\mathrm{R}\left(\frac{2\mathrm{gR}}{{\mathrm{v}}^2}-1\right)$