- 1(current)
Q. No.| 1. | \(\dfrac{v}{3}\) | 2. | \(\dfrac{2v}{3}\) |
| 3. | \(\dfrac{3v}{4}\) | 4. | \(\dfrac{9v}{4}\) |
(given, the radius of Earth \(=6400~\text{km}\) )
1. \(1600~\text{km}\)
2. \(3200~\text{km}\)
3. \(6400~\text{km}\)
4. \(12800~\text{km}\)
| 1. | \(11.2\sqrt2~\text{km/s}\) | 2. | zero |
| 3. | \(11.2~\text{km/s}\) | 4. | \(11.2\sqrt3~\text{km/s}\) |
The escape velocity from the Earth's surface is \(v\). The escape velocity from the surface of another planet having a radius, four times that of Earth and the same mass density is:
| 1. | \(3v\) | 2. | \(4v\) |
| 3. | \(v\) | 4. | \(2v\) |
A particle of mass \(m\) is projected with a velocity, \(v=kv_{e} ~(k<1)\) from the surface of the earth. The maximum height, above the surface, reached by the particle is:
(Where \(v_e=\) escape velocity, \(R=\) the radius of the earth)
| 1. | \(\dfrac{R^{2}k}{1+k}\) | 2. | \(\dfrac{Rk^{2}}{1-k^{2}}\) |
| 3. | \(R\left ( \dfrac{k}{1-k} \right )^{2}\) | 4. | \(R\left ( \dfrac{k}{1+k} \right )^{2}\) |
1. \(1:2\sqrt{2}\)
2. \(1:4\)
3. \(1:\sqrt{2}\)
4. \(1:2\)
A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would Earth (mass\(m=5.98\times 10^{24}~\text{kg})\) have to be compressed to be a black hole?
1. \(10^{-9}~\text{m}\)
2. \(10^{-6}~\text{m}\)
3. \(10^{-2}~\text{m}\)
4. \(100~\text{m}\)
| 1. | \(v_P = 1.5 v_E\) | 2. | \(v_P = 2v_E\) |
| 3. | \(v_E = 3 v_P\) | 4. | \(v_E = 1.5v_P\) |
(where \(g\) is the acceleration due to gravity on the surface of the Earth)
| 1. | \(\left(\dfrac{{GM}}{2 {R}}\right)^{\frac{1}{2}} \) | 2. | \(\left(\dfrac{{g} R}{4}\right)^{\frac{1}{2}} \) |
| 3. | \( \left(\dfrac{2 g}{R}\right)^{\frac{1}{2}} \) | 4. | \(\left(\dfrac{G M}{R}\right)^{\frac{1}{2}}\) |
- 1(current)
Q. No.
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