NEET Solved Paper 2014 Question 11
Question: 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 = $ 5.98\times 10^{24}kg $ kg) have to be compressed to be a black hole? [AIPMT 2014]
Options:
A) $ {10^{-9}}m $
B) $ {10^{-6}}m $
C) $ {10^{-2}}m $
D) 100 m
Show Answer
Answer:
Correct Answer: C
Solution:
- Problem Solving Strategy For the black hole, the escape speed is more than c (speed of light). We should compare the escape speed with the (Note that the escape speed should be at least just greater than c.) $ v _{e}=\sqrt{\frac{2GM}{R’}}[R’\to $ New radius of the earth] $ c=\sqrt{\frac{2GM}{R’}}[v _{e}\approx c] $
$ \Rightarrow $ $ c^{2}=2\frac{GM}{R’} $ $ R’=\frac{2GM}{c^{2}}=\frac{2\times 6.67\times {10^{-11}}\times 6\times 10^{24}}{9\times 10^{16}} $ $ =\frac{4\times 6.67}{3}\times {10^{-3}} $ $ =8.89\times {10^{-3}} $ $ =0.889\times {10^{-2}} $ $ \simeq {10^{-2}}m $
