Two astronauts are floating in a gravitational free space after having lost contact with their spaceship. The two will:
1. | keep floating at the same distance between them |
2. | move towards each other |
3. | move away from each other |
4. | will become stationary |
A remote sensing satellite of the earth revolves in a circular orbit at a height of 0.25 x 106 m above the surface of the earth. If the earth’s radius is 6.38x106 m and g=9.8ms-1, then the orbital speed of the satellite is:
1. 7.76 kms-1
2. 8.56 kms-1
3. 9.13 kms-1
4. 6.67 kms-1
The radii of the circular orbits of two satellites A and B of the earth are \(4R\) and \(R,\) respectively. If the speed of satellite A is \(3v,\) then the speed of satellite B will be:
1. | \(3v/4\) | 2. | \(6v\) |
3. | \(12v\) | 4. | \(3v/2\) |
If the acceleration due to gravity at a height \(1\) km above the earth is similar to a depth \(d\) below the surface of the earth, then:
1. \(d= 0.5\) km
2. \(d=1\) km
3. \(d=1.5\) km
4. \(d=2\) km
If the gravitational force between two objects were proportional to \(\frac{1}{R}\) (and not as\(\frac{1}{R^2}\)) where \(R\) is the separation between them, then a particle in circular orbit under such a force would have its orbital speed \(v\) proportional to:
1. \(\frac{1}{R^2}\)
2. \(R^{0}\)
3. \(R^{1}\)
4. \(\frac{1}{R}\)
A satellite is launched into a circular orbit of radius \(R\) around the Earth while a second satellite is launched into an orbit of radius \(1.02~\text{R}\). The percentage difference in the time periods of the two satellites is:
1. | \(0.7\) | 2. | \(1.0\) |
3. | \(1.5\) | 4. | \(3\) |
A body is projected vertically upwards from the surface of a planet of radius \(R\) with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is:
1. \(\frac{R}{3}\)
2. \(\frac{R}{2}\)
3. \(\frac{R}{4}\)
4. \(\frac{R}{5}\)
A body of mass \(m\) kg starts falling from a point \(2R\) above the Earth’s surface. Its kinetic energy when it has fallen to a point \(R\) above the Earth’s surface, is:
[\(R\text-\) Radius of Earth, \(M\text-\) Mass of Earth, \(G\text-\) Gravitational Constant]
1. \(\frac{1}{2} \frac{G M m}{R}\)
2. \(\frac{1}{6} \frac{G M m}{R}\)
3. \(\frac{2}{3} \frac{G M m}{R}\)
4. \(\frac{1}{3} \frac{G M m}{R}\)
The orbital angular momentum of a satellite revolving at a distance \(r\)from the centre is \(L\). If the distance is increased to 16r, then the new angular momentum will be:
1. | \(16~L\) | 2. | \(64~L\) |
3. | \(L \over 4\) | 4. | \(4~L\) |
Two satellites A and B go around the earth in circular orbits at heights of respectively from the surface of the earth. Assuming earth to be a uniform sphere of radius , the ratio of the magnitudes of their orbital velocities is:
1.
2.
3.
4.