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Q. No.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. | \(\left(\dfrac{G M}{R}\right)^{\frac{1}{2}}\) |
A particle of mass \(m\) is thrown upwards from the surface of the earth, with a velocity \(u.\) The mass and the radius of the earth are, respectively, \(M\) and \(R.\) \(G\) is the gravitational constant and \(g\) is the acceleration due to gravity on the surface of the earth. The minimum value of \(u\) so that the particle does not return back to earth is:
1. \(\sqrt{\dfrac{2 {GM}}{{R}^2}} \)
2. \(\sqrt{\dfrac{2 {GM}}{{R}}} \)
3.\(\sqrt{\dfrac{2 {gM}}{{R}^2}} \)
4. \(\sqrt{ {2gR^2}}\)
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 \(fv_e\), where \(v_e\) is its escape velocity from the surface of the earth. The value of \(f\) is:
1. \(\sqrt{2}\)
2. \(\frac{1}{\sqrt{2}}\)
3. \(\frac{1}{3}\)
4. \(\frac{1}{2}\)
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Q. No.
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