Question

Black holes with masses smaller than those formed in supernovas may have been created in the Big Bang. Calculate the radius of one that has a mass equal to the Earth’s.

a)8.9mm
b)8.9km
c)8.9cm
d)8.9μm

Answer 1

To calculate the radius of a black hole with mass equal to the Earth's, use the formula for the Schwarzschild radius. For the Earth, the radius would be approximately 8.9 millimeters.

Therefore, the correct answer is a) 8.9mm.

Step-by-step explanation:

To calculate the radius of a black hole with mass equal to the Earth's, we can use the formula for the Schwarzschild radius:

r = (2GM)/(c^2)

where G is the gravitational constant, M is the mass of the black hole, and c is the speed of light.

For the Earth, we can assume a mass of approximately 5.972 x 10^24 kilograms. Plugging this value into the formula, along with the constants G = 6.67430 x 10^-11 m^3 kg^-1 s^-2 and c = 299,792,458 m/s, we can calculate the radius:

r = (2 x 6.67430 x 10^-11 x 5.972 x 10^24)/(299,792,458^2)

Calculating this expression gives us a value of approximately 8.9 millimeters (mm).

Therefore, the correct answer is a) 8.9mm.