First slide

Gravitaional potential energy

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 x $10^{24}$ kg) have to be compressed to be a black hole?

Moderate

Solution

$\begin{aligned} Light cannot escape from a black hole, \\ \frac{v_{esc} = c}{\sqrt{\frac{2 G M}{R}}} = c or R = \frac{2 G M}{c^{2}} \end{aligned}$
$\begin{aligned} R = \frac{2 \times 6.67 \times 10^{- 11} {Nm}^{2} {kg}^{- 2} \times 5.98 \times 10^{24} kg}{{(3 \times 10^{8} {ms}^{- 1})}^{2}} \\ = 8.86 \times 10^{- 3} m \approx 10^{- 2} m \end{aligned}$

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