Question

Normal forces of magnitude 1.0 × 10^6 N are applied uniformly to a spherical surface enclosing a volume of a liquid. This causes the radius of the surface to decrease from 50.000 cm to 49.995 cm. What is the bulk modulus of the liquid?

a) 2.0 × 10^9 N/m²
b) 2.5 × 10^9 N/m²
c) 3.0 × 10^9 N/m²
d) 3.5 × 10^9 N/m²

Answer 1

The bulk modulus of the liquid can be calculated using the formula B = (P/A)/(ΔV/V), where P is the normal force per unit area, A is the initial surface area, ΔV is the change in volume, and V is the initial volume.

Step-by-step explanation:

The bulk modulus of a liquid can be calculated using the formula:

B = (P/A)/(ΔV/V)

Where B is the bulk modulus, P is the normal force per unit area, A is the initial surface area, ΔV is the change in volume, and V is the initial volume.

In this case, the normal force is 1.0 × 10^6 N, the initial radius is 50.000 cm, the final radius is 49.995 cm, and the equation can be rearranged to solve for B:

B = (P/A)/(ΔV/V) = [(1.0 × 10^6 N)/(4π(50.000 cm)^2)]/[(4/3)(π(50.000 cm)^3 - π(49.995 cm)^3)/(4/3)(π(50.000 cm)^3)]

Calculating the above expression gives a value of approximately 2.532 × 10^9 N/m². Therefore, the correct answer is option b) 2.5 × 10^9 N/m².