Question

how small would mount everest have to shrink for it to become a black hole?
to a radius of one nanometer (1 billionth of a meter)
to a radius of one inch
to a radius of nine feet
to a radius of 19 miles

Explanation:

Step1: Recall Schwarzschild radius formula

The Schwarzschild radius formula for a non - rotating mass \(M\) is \(R_s=\frac{2GM}{c^{2}}\), where \(G = 6.67\times10^{- 11}\ m^{3}kg^{-1}s^{-2}\) is the gravitational constant, \(M\) is the mass of the object, and \(c = 3\times10^{8}\ m/s\) is the speed of light. The mass of Mount Everest is approximately \(M = 3\times10^{12}\ kg\).

Step2: Substitute values into formula

\[

$$\begin{align*} R_s&=\frac{2\times6.67\times10^{-11}\times3\times 10^{12}}{(3\times10^{8})^{2}}\\ &=\frac{40.02\times10^{1}}{9\times10^{16}}\\ &=\frac{400.2}{9\times10^{16}}\\ &\approx4.45\times 10^{-15}\ m \end{align*}$$

\]
1 nanometer \(= 1\times10^{-9}\ m\), 1 inch \(= 0.0254\ m\), 9 feet \(=9\times0.3048 = 2.7432\ m\), 19 miles \(=19\times1609.34 = 30577.46\ m\). A more accurate way for a general - knowledge estimate: For an object to become a black - hole, it needs to be compressed to its Schwarzschild radius. For a mountain - sized object like Mount Everest, it would need to be compressed to an extremely small size. The order of magnitude of the Schwarzschild radius for Mount Everest is very small. The closest reasonable order of magnitude among the options for a very small radius is one nanometer.

Answer:

to a radius of one nanometer (1 billionth of a meter)