To solve this problem, we need to find the temperature at which the diameter of the steel sphere becomes equal to the diameter of the aluminum ring.

The formula for linear expansion is ΔL = αL0ΔT, where ΔL is the change in length, α is the coefficient of linear expansion, L0 is the initial length, and ΔT is the change in temperature.

In this case, we want the final diameters of the sphere and the ring to be equal, so we set their ΔL equal to each other:

α_steel * D_steel * ΔT = α_aluminum * D_aluminum * ΔT

We can solve this equation for ΔT:

ΔT = (α_aluminum * D_aluminum - α_steel * D_steel) / (α_steel - α_aluminum)

Substituting the given values:

ΔT = ((2.40 × 10−5/°C * 3.9900 cm) - (1.10 × 10−5/°C * 4.0000 cm)) / (1.10 × 10−5/°C - 2.40 × 10−5/°C)

Solving this equation gives ΔT ≈ 116°C.

So, the sphere will just fall through the ring at a temperature increase of approximately 116°C from 0°C, which is a final temperature of 116°C.

Therefore, the correct answer is c. 116°C.

Question

To solve this problem, we need to find the temperature at which the diameter of the steel sphere becomes equal to the diameter of the aluminum ring.

The formula for linear expansion is ΔL = αL0ΔT, where ΔL is the change in length, α is the coefficient of linear expansion, L0 is the initial length, and ΔT is the change in temperature.

In this case, we want the final diameters of the sphere and the ring to be equal, so we set their ΔL equal to each other:

α_steel * D_steel * ΔT = α_aluminum * D_aluminum * ΔT

We can solve this equation for ΔT:

ΔT = (α_aluminum * D_aluminum - α_steel * D_steel) / (α_steel - α_aluminum)

Substituting the given values:

ΔT = ((2.40 × 10−5/°C * 3.9900 cm) - (1.10 × 10−5/°C * 4.0000 cm)) / (1.10 × 10−5/°C - 2.40 × 10−5/°C)

Solving this equation gives ΔT ≈ 116°C.

So, the sphere will just fall through the ring at a temperature increase of approximately 116°C from 0°C, which is a final temperature of 116°C.

Therefore, the correct answer is c. 116°C.

Knowee AI · Accepted Answer