Question

Normal forces are applied uniformly over the surface of a spherical volume of water whose radius is 20.0 cm. If the pressure on the surface is increased by 200 MPa, by how much does the radius of the sphere decrease?

a) 0.10 mm
b) 0.25 mm
c) 0.50 mm
d) 1.00 mm

Answer 1

To determine the change in radius of a spherical volume of water based on an increase in pressure on the surface, we can use the formula for pressure, force, and radius. By substituting the given values into the formula, we can calculate the force applied over the surface of the sphere. Using the relationship between force and the change in radius, we can then determine the change in radius of the sphere.

Step-by-step explanation:

To solve this problem, we can use the relationship between pressure and radius for a spherical object. According to the problem, the pressure on the surface of the spherical volume of water is increased by 200 MPa. We can use the formula for pressure, which is given by P = F/A (where P is the pressure, F is the force, and A is the area). We can rearrange the formula to solve for force, which is given by F = P * A. Since the normal forces are applied uniformly over the surface of the sphere, the force can be written as F = P * 4πr^2, where r is the radius of the sphere.

By substituting the given values into the formula, we get F = (200 x 10^6 N/m^2) x (4π x (0.2 m)^2). Evaluating this equation will give us the force applied over the surface of the sphere.

Now, we know that the force is related to the change in radius of the sphere. According to the formula for force, pressure, and radius, F = k * ∆r, where k is a constant. By rearranging the formula, we get ∆r = F / k. Since the problem asks for the change in radius, we can solve for ∆r using the force calculated earlier and dividing it by k.