Two compressible solids are formed into spheres of the same size. The bulk modulus of sphere two is twice as large as the bulk modulus of sphere one. You now increase the pressure on both spheres by the same amount. As a result of the increased pressure, how is the change in volume of sphere two (△V₂) related to the change in volume of sphere one (ΔV₁)? A) ΔV₂= 2ΔV₁ B) ΔV₂ = 4ΔV₁ C) vV₂= ΔV₁ D) ΔV₂ = 1/2ΔV₁ E) ΔV₂ = 1/4ΔV₁

Question

Quizplus · Accepted Answer

According to the formula for the change in volume of a sphere under pressure, ΔV = -V(ΔP/B). Since the spheres are the same size, their volumes are the same initially. Thus, the ratio of their volume changes will be determined solely by the ratio of their bulk moduli. We are given that the bulk modulus of sphere two is twice that of sphere one, so B2/B1 = 2. Plugging this into the formula and solving for ΔV2/ΔV1, we get:

ΔV2/ΔV1 = -V(ΔP/B2) / (-V(ΔP/B1)) = B1/B2 = 1/2

Therefore, the change in volume of sphere two is half that of sphere one, so the answer is D.

Two Compressible Solids Are Formed into Spheres of the Same