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 l x 1011 kg (and a radius of only 1 x l0-16 m) reached earth, at what distance from your head would its gravitational pull on you match that of earth's?

The distance as calculated is 0.823 m

Solution:

As per the question:

Mass of black hole, M =

Radius of blck hole, R =

Now,

At the time when the black hole's gravitational force exerts a pull on the body, the gravitational force due to Earth on the body and that due to black hole will be the same.

Gravitational force due to Earth is given by:

where

M' = Mass of earth

m = Mass of the body

R' = Separation distance between the body and the center of the Earth

Now,

Gravitational force of the black hole on the body is given by:

Now,

                    (1)

where

                                         (2)

From the eqn (1) and (2):

R = 0.823 m

gpe = mass x gravity constant x height or… gpe = mgh

where… mass: measured in kilograms (kg)

gravity: gravity constant on earth = 10.00 m/s2

height: measured in meters (m)

gpe: measured in joules (j) or kilojoules (kj)

how do you solve gpe?

gravitational potential energy (gpe) is the energy an object has because of its position above the. ground.

gpe = mass x gravity constant x height or… gpe = mgh.

mass:

note: to earn full marks when solving science word problems, you must show your work:

formula.

example:

given values:

mass = 0.3 kg.