To what radius would the sun have to be compressed in order for it to become a black hole? The mass of the sun is $1.99 \times 10 ^ { 30 } \mathrm {~kg} , G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 }$, and $c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$
A) $6.96 \times 10 ^ { 8 } \mathrm {~m}$
B) $2950 \mathrm {~m}$
C) $3.72 \times 10 ^ { 4 } \mathrm {~m}$
D) $2.66 \times 10 ^ { 6 } \mathrm {~m}$
E) $1470 \mathrm {~m}$

Question

Quizplus · Accepted Answer

The radius to which the Sun must be compressed to form a black hole can be found using the Schwarzschild radius formula: $R = \frac{2GM}{c^2}$. Substituting the given values: $R = \frac{2 \times 6.67 \times 10^{-11} \mathrm{N\cdot m^2/kg^2} \times 1.99 \times 10^{30} \mathrm{kg}}{(3.00 \times 10^8 \mathrm{m/s})^2}$, we find $R \approx 2950 \mathrm{m}$.

To What Radius Would the Sun Have to Be Compressed 1.99×1030 kg,G=6.67×10−11 N⋅m2/kg21.99 \times 10 ^ { 30 } \mathrm {~kg} , G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 }1.99×1030 kg,G=6.67×10−11 N⋅m2/kg2

To What Radius Would the Sun Have to Be Compressed $1.99 \times 10 ^ { 30 } \mathrm {~kg} , G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 }$