AIIMS AIIMS Solved Paper-2005

  • question_answer
                                   The condition for a uniform spherical mass m of radius r to be a black hole is: [G = gravitational constant and g= acceleration due to gravity]

    A)  \[-0.1\left[ \frac{{{(30)}^{2}}}{2}-\frac{{{(20)}^{2}}}{2} \right]={{K}_{f}}-500\]    

    B)       \[\Rightarrow \]              

    C)       \[{{K}_{f}}-500=-25\]     

    D)       \[\Rightarrow \]

    Correct Answer: C

    Solution :

                    A black hole is an object so massive that even light cannot escape from it. This requires the idea of a gravitational mass for a photon, which then allows the calculation of an escape energy, for an object of that mass. When gravitational potential energy of the photon is exactly equal to the photon energy, then \[2\sigma /{{\varepsilon }_{0}}V/m\]                  ??(1) where G is gravitational constant, M is mass, r is radius, c is speed of light, h is Plancks constant. Then from Eq. (1) we have \[{{\mu }_{e}}\] Note that this condition is independent of frequency v.  Schwarz childs calculated gravitational radius differs from this result by a factor of 2 and is coincidently equal to the non-relativistic escape velocity expression. \[{{\mu }_{h}}\]


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