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:
1. | \(\frac{\mathrm{GMm}}{\mathrm{12R}} \) | 2. | \(\frac{\mathrm{GMm}}{\mathrm{R}} \) |
3. | \(\frac{\mathrm{GMm}}{8 \mathrm{R}} \) | 4. | \(\frac{\mathrm{GMm}}{2 \mathrm{R}}\) |
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:-
1. | \(Gm^2\over r\) | 2. | \(3Gm^2\over r\) |
3. | \({3 \over 2}{Gm^2\over r}\) | 4. | None |
If the radius of a planet is \(\mathrm{R}\) and its density is , the escape velocity from its surface will be:
1.
2.
3.
4.
The gravitational force between two point masses and at separation r is given by
The constant k:
1. | depends on the system of units only. |
2. | depends on the medium between masses only. |
3. | depends on both (a) and (b). |
4. | is independent of both (a) and (b). |
The centripetal force acting on a satellite orbiting around the earth and the gravitational force of the earth acting on the satellite, both are equal to F. The net force on the satellite is:
1. Zero
2. F
3.
4. 2 F
Two identical solid copper spheres of radius R are placed in contact with each other. The gravitational attraction between them is proportional to
1.
2.
3.
4.
An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy . Its potential energy is?
1.
2.
3.
4.
An object weighs 72 N on earth. Its weight at a height R/2 from the surface of the earth will be:
1. | 32 N | 2. | 56 N |
3. | 72 N | 4. | Zero |
Mass \(M\) is divided into two parts \(xM\) and \((1-x)M.\) For a given separation, the value of \(x\) for which the gravitational attraction between the two pieces becomes maximum is:
1. | \(\frac{1}{2}\) | 2. | \(\frac{3}{5}\) |
3. | \(1\) | 4. | \(2\) |
Two particles of equal masses go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is:
1.
2.
3.
4.