Solveeit Logo
Login

Question

Physics Question on Gravitation

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 =5.98×1024 kg= 5.98 \times 10^{24} \, kg) have to be compressed to be a black hole?

A

10−9 m10^{-9} \, m

B

10−6 m10^{-6} \, m

C

10−2 m10^{-2} \, m

D

100 m100\, m

Answer

10−2 m10^{-2} \, m

Explanation

Solution

Light cannot escape from a black hole,
vesc=cv_{esc} = c
2GMR=c\sqrt \frac {2GM}{R} = c or R=2GMc2R = \frac {2GM}{c^2}
R=2 × 6.67×10−11 N m2 kg−2 × 5.98 × 1024 kg(3 × 108 ms−1)2R = \frac {2\, \times \,6.67 \times 10^{-11}\,N \,m^2\, kg^{-2}\, \times \,5.98\, \times \,10^{24}\,kg}{(3 \,\times \,10^8 \,ms^{-1})^2}
=8.86×10−3 m≈10−2 m= 8.86 \times 10^{-3} \,m \approx 10 ^{-2}\, m