A satellite of mass m is orbiting the earth [of radius R] at a height h from its surface. The total energy of the satellite in terms of $g_o$, the value of acceleration due to gravity at the earth's surface is -

1. $\frac{m{g}_o{R}^2}{2\left(R+h\right)}$

2. $-\frac{m{g}_o{R}^2}{2\left(R+h\right)}$

3. $\frac{2m{g}_o{R}^2}{R+h}$

4. $-\frac{2m{g}_o{R}^2}{2\left(R+h\right)}$

The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is:

1. $\frac{3}{2}mgR$

2. mgR

3. 2mgR

4. $\frac{1}{2}mgR$

A body of mass m rises to height h = R/5 from the earth's surface, where R is earth's radius. If g is acceleration due to gravity at earth's surface, the increase in potential energy is -

1. mgh                                 

2. $\frac{4}{5}mgh$

3. $\frac{5}{6}mgh$                             

4. $\frac{6}{7}mgh$

If a body of mass m placed on the earth's surface is taken to a height of h = 3R, then the change in gravitational potential energy is:

1. $\frac{\mathrm{mgR}}{4}$

2. $\frac{2}{3}\mathrm{mgR}$

3. $\frac{3}{4}\mathrm{mgR}$

4. $\frac{\mathrm{mgR}}{2}$

A particle is dropped from a height h = 3R above the earth's surface, where R is the radius of the earth. If g is the acceleration due to gravity on the earth surface, then the speed with which the particle strikes the earth surface is:

1.  $\sqrt{3gR}$

2.  $\sqrt{2gR}$

3.  $\sqrt{1.5gR}$

4.  $\sqrt{gR}$

A body of mass \(m\) is taken from the earth's surface to the height \(h\) equal to the radius of the earth, the increase in potential energy will be:
1. \(mgR\)
2. \(\frac{1}{2}~mgR\)
3. \(2 ~mgR\)
4. \(\frac{1}{4}~mgR\)

When a body of mass m is lifted from the surface of the earth to a height equal to radius R of the earth, the change in gravitational potential energy of the body is (g: acceleration due to gravity at the surface of the earth):

(1) $\frac{1}{2}$ mgR

(2) mgR

(3) 3 mgR

(4) 2 mgR

The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is:

1. $\frac{3}{2}mgR$

2. mgR

3. 2mgR

4. $\frac{1}{2}mgR$