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 `=5.98xx10^(24)kg`) have to be compresed to be a black hole?
A. `10^(-9)m`
B. `10^(-6)m`
C. `10^(-2)m`
D. `100 m`

Answer 1

Correct Answer - C
The earth will become black hole if the escape velocity on earth is equal to the velocity of light,
i.e., `upsilon_(e) = sqrt((2GM)/(R )) = c` or `R = (2GM)/(c^(2))`
`:. R = (2 xx (6.67 xx 10^(-11)) xx (5.98 xx 10^(24)))/((3 xx 10^(8))^(2))`
`= 8.86 xx 10^(-3) m ~~ 10^(-2)m`.