A satellite of mass \(M\) is revolving around the Earth in a stationary orbit with a time period \(T.\) If \(10\%\) of the satellite's mass is detached, what will happen to its time period?
1. remain the same
2. increase by \(10\%\)
3. decrease by \(10\%\)
4. decrease by \(20\%\)
1. | \(\frac{2 G m M}{3 R} \) | 2. | \(\frac{G m M}{2 R} \) |
3. | \(\frac{G m M}{3 R} \) | 4. | \( \frac{5 G m M}{6 R}\) |
1. | \(6 . 48 \times 10^{23} \text{ kg}\) | 2. | \(6 . 48 \times 10^{25} \text{ kg}\) |
3. | \(6 . 48 \times 10^{20} \text{ kg}\) | 4. | \(6 . 48 \times 10^{21} \text{ kg}\) |
A planet is orbiting the sun in an elliptical orbit. Let \(U\) denote the potential energy and \(K\) denote the kinetic energy of the planet at an arbitrary point in the orbit.
Choose the correct statement from the given ones:
1. | \(K<\left| U\right|\) always |
2. | \(K>\left| U\right|\) always |
3. | \(K=\left| U\right|\) always |
4. | \(K=\left| U\right|\) for two positions of the planet in the orbit |
Satellites orbiting the earth have a finite life and sometimes debris of satellites fall to the earth. This is because:
1. | the solar cells and batteries in satellites run out. |
2. | the laws of gravitation predict a trajectory spiralling inwards. |
3. | of viscous forces causing the speed of the satellite and hence height to gradually decrease. |
4. | of collisions with other satellites. |
1. | \(3.13\times10^{9}~\text{J}\) | 2. | \(3.13\times10^{10}~\text{J}\) |
3. | \(4.13\times10^{9}~\text{J}\) | 4. | \(4.13\times10^{8}~\text{J}\) |