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

Step-by-step explanation:

It is given that,

Mass,
`M=3* 10^(11)\ kg`

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

Acceleration due to gravity is given by :

`g=(GM)/(r^2)`

r = distance from head

`r=\sqrt{(GM)/(g)}`

`r=\sqrt{(6.67* 10^(-11)* 3* 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.