1. | \(\frac{GMm}{12R} \) | 2. | \(\frac{GMm}{R} \) |
3. | \(\frac{GMm}{8 R} \) | 4. | \(\frac{GMm}{2R}\) |
Three equal masses \(m\) are placed at the three vertices of an equilateral triangle of side \(r\). 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 of the above |
If the radius of a planet is \(R\) and its density is \(\rho\), the escape velocity from its surface will be:
1. \(v_e\propto \rho R\)
2. \(v_e\propto \sqrt{\rho} R\)
3. \(v_e\propto \frac{\sqrt{\rho}}{R}\)
4. \(v_e\propto \frac{1}{\sqrt{\rho} R}\)
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. \(F\sqrt{2}\)
4. \(2F\)
Two identical solid copper spheres of radius \(R\) are placed in contact with each other. The gravitational attraction between them is proportional to:
1. \(R^2\)
2. \(R^{-2}\)
3. \(R^4\)
4. \(R^{-4}\)
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. \(v = \frac{1}{2 R} \sqrt{\frac{1}{Gm}}\)
2. \(v = \sqrt{\frac{Gm}{2 R}}\)
3. \(v = \frac{1}{2} \sqrt{\frac{G m}{R}}\)
4. \(v = \sqrt{\frac{4 Gm}{R}}\)