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 3.5 1011 kg (and a radius of only 1.0 10-14 m) reached Earth, at what distance from your head would its gravitational pull on you match that of Earth's?

...I'm not sure how to go about solving this...

9.8=G3.5E11/r^2 solve for r

To solve this problem, we can use the concept of gravitational attraction. The gravitational force between two objects depends on their masses and the distance between them. In this case, we need to find the distance at which the gravitational pull of the tiny black hole matches that of the Earth.

Here's how we can approach the problem:

Step 1: Find the gravitational force of the tiny black hole on you

The formula to calculate the gravitational force between two objects is given by:

F = G * (m1 * m2) / r^2

Where:
F is the force of gravity
G is the gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the objects

In this case, the mass of the tiny black hole is given as 3.5 * 10^11 kg. As the force needs to be equal to the gravitational pull of the Earth, we can set up the equation as follows:

F = (G * (m1 * mEarth) / r^2) = mEarth * g

Where:
mEarth is the mass of the Earth (approximately 5.972 × 10^24 kg)
g is the acceleration due to gravity on Earth (approximately 9.8 m/s^2)

Step 2: Solve for r

Rearranging the equation from step 1, we can isolate the distance r:

r = sqrt((G * m1 * mEarth) / (mEarth * g))

Step 3: Calculate the distance

Plug in the known values and calculate the distance. Note that the units need to be consistent throughout the calculation (e.g., kilograms for mass and meters for distance).

r = sqrt((6.674 × 10^-11 N m^2/kg^2 * (3.5 × 10^11 kg) * (5.972 × 10^24 kg)) / ((5.972 × 10^24 kg) * (9.8 m/s^2)))

Evaluate the expression to find the distance r, which will give you the answer to the question.

I hope this explanation helps you understand how to solve the problem.