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) have to be compressed to be a black hole?

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 × 1024 kg) have to be compressed to be a black hole? (A) 10-9 m (B) 10-6 m (C) 10-2 m (D) 100 m

Tardigrade Admin · Accepted Answer

Light cannot escape from a black hole, v textesc =c √(2 G M/R)=c or R=(2 G M/c2) R=(2 × 6.67 × 10-11 N m 2 kg -2 × 5.98 × 1024 kg /(3 × 108 m s -1)2) =8.86 × 10-3 m ≈ 10-2 m

Q. 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 $= 5.98 \times 1 0^{24} k g$ ) have to be compressed to be a black hole?

$1 0^{- 9} m$

$1 0^{- 6} m$

$1 0^{- 2} m$

$100 m$

Light cannot escape from a black hole,
$v_{esc} = c$
$\frac{2 GM}{R} = c$
or $R = \frac{2 GM}{c ^{2}}$
$R = \frac{2 \times 6.67 \times 1 0 ^{- 11} N m ^{2} k g ^{- 2} \times 5.98 \times 1 0 ^{24} k g}{( 3 \times 1 0 ^{8} m s ^{- 1} ) ^{2}}$
$= 8.86 \times 1 0^{- 3} m \approx 1 0^{- 2} m$

Q. 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 =5.98×1024kg) have to be compressed to be a black hole?

10−9m

10−6m

10−2m

100m