Question

Left over from the big-bang beginning of the universe, tiny black holes might still wander through the universe. If one with a mass of 3 × 10^11 kg (and a radius of only 1 × 10^-16 m) reached Earth, at what distance from your head would its gravitational pull on you match that of Earth's? Assume free-fall acceleration ag=9.83 m/s2.

Answer 1

Explanation:

It is given that,

Mass, $M=3\times 10^{11}\ kg$

Acceleration due to gravity, $g=9.8\ m/s^2$

Acceleration due to gravity is given by :

$g=\dfrac{GM}{r^2}$

r = distance from head

$r=\sqrt{\dfrac{GM}{g}}$

$r=\sqrt{\dfrac{6.67\times 10^{-11}\times 3\times 10^{11}}{9.8}}$

r = 1.42 m

So, at the distance of 1.42 meters from the head its gravitational pull on you match that of Earth's. Hence, this is the required solution.