Question

The tympanic membrane (ear drum) is a very delicate component of the human ear. Typically, its diameter is ∼1cm. The maximum force the ear can withstand is 2.5N. In case a diver has to enter sea water of density 1.05⋅103kg/m^3 without any protective gear, the maximum safe depth for the diver to go into the water is about ______?

I was not able to get the correct answer using p=rhogh, where p is pressure. Will the diameter given be used?

Answer 1

To determine the maximum safe depth for the diver to go into the water, we need to calculate the pressure the ear drum can withstand and use it to find the depth using the given formula.

Step-by-step explanation:

To determine the maximum safe depth for the diver to go into the water, we need to calculate the pressure the ear drum can withstand using the formula p = ρgh (where p is pressure, ρ is density, g is gravitational acceleration, and h is depth).

First, we need to convert the force of 2.5N to pressure by dividing it by the area of the eardrum. Since the eardrum has a diameter of 1cm, its area can be calculated as A = πr^2, where r is the radius of the eardrum.

Once we have the pressure, we can rearrange the formula p = ρgh to solve for the depth h. Substitute the given density and solve for h.

This will give us the maximum safe depth for the diver to go into the water without any protective gear.