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?

Options

A. `10^(-9) m`
B. `10^(-6) m`
C. `10^(-2) m`
D. `100m`

Answer

C

Explanation

Light cannot escape from a black hole, `v_(esc) = c`
` sqrt((2GM)/( R)) c " or " R = (2GM)/(c^2)`
` R = (2 xx 6.67 xx 10^(-11) Nm^2 kg^(-2) xx 5.98 xx 10^24 kg)/((3 xx 10^8 ms^(-1) )^2)`
` = 8.86 xx 10^(-3)m ~~ 10^(-2) m`