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 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 |
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.
A body weighs \(200\) N on the surface of the earth. How much will it weigh halfway down the centre of the earth?
1. | \(100\) N | 2. | \(150\) N |
3. | \(200\) N | 4. | \(250\) N |
The earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the earth. The escape velocity of a body from this platform is fve, where ve is its escape velocity from the surface of the earth. The value of f is:
1.
2.
3.
4.
Two satellites of Earth, \(S_1\), and \(S_2\), are moving in the same orbit. The mass of \(S_1\) is four times the mass of \(S_2\). Which one of the following statements is true?
1. | The time period of \(S_1\) is four times that of \(S_2\). |
2. | The potential energies of the earth and satellite in the two cases are equal. |
3. | \(S_1\) and \(S_2\) are moving at the same speed. |
4. | The kinetic energies of the two satellites are equal. |
The figure shows the elliptical orbit of a planet \(m\) about the sun \(\mathrm{S}.\) The shaded area \(\mathrm{SCD}\) is twice the shaded area \(\mathrm{SAB}.\) If \(t_1\) is the time for the planet to move from \(\mathrm{C}\) to \(\mathrm{D}\) and \(t_2\) is the time to move from \(\mathrm{A}\) to \(\mathrm{B},\) then:
1. | \(t_1>t_2\) | 2. | \(t_1=4t_2\) |
3. | \(t_1=2t_2\) | 4. | \(t_1=t_2\) |