A) \[{{10}^{-9}}m\]
B) \[{{10}^{-6}}m\]
C) \[{{10}^{-2}}m\]
D) 100 m
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] \[c=\sqrt{\frac{2GM}{R'}}[{{v}_{e}}\approx c]\] \[\Rightarrow \] \[{{c}^{2}}=2\frac{GM}{R'}\] \[R'=\frac{2GM}{{{c}^{2}}}=\frac{2\times 6.67\times {{10}^{-11}}\times 6\times {{10}^{24}}}{9\times {{10}^{16}}}\] \[=\frac{4\times 6.67}{3}\times {{10}^{-3}}\] \[=8.89\times {{10}^{-3}}\] \[=0.889\times {{10}^{-2}}\] \[\simeq {{10}^{-2}}m\]
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