The brass disc fits singly in a hole in a steel plate. To loose the disk from hole

Options

A. we should heat the system
B. we should cool the system
C. we should apply a strong external force
D. it can not be separated

Answer

To solve the problem of loosening a brass disc that fits snugly in a hole in a steel plate, we need to consider the principles of thermal expansion. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the concept of thermal expansion
When materials are heated, they expand, and when they are cooled, they contract. The degree to which a material expands or contracts is characterized by its coefficient of thermal expansion (γ).

### Step 2: Identify the coefficients of thermal expansion
For brass, the coefficient of volume expansion (γ) is approximately \( 3 \times 10^{-5} \, \text{°C}^{-1} \), and for steel, it is approximately \( 1.2 \times 10^{-5} \, \text{°C}^{-1} \). This means that brass expands and contracts more than steel for the same change in temperature.

### Step 3: Determine the effect of heating
If we heat both the brass disc and the steel plate, the brass will expand more than the steel due to its higher coefficient of thermal expansion. This means that the disc will fit even tighter in the hole, making it more difficult to remove.

### Step 4: Determine the effect of cooling
Conversely, if we cool the system, both the brass and steel will contract. However, since brass has a higher coefficient of thermal expansion, it will contract more than steel. This means that the disc will loosen and can be removed from the hole.

### Step 5: Conclusion
To loosen the brass disc from the hole in the steel plate, we should cool down the system. This will allow the brass disc to shrink more than the steel hole, making it easier to remove.

### Final Answer:
To loosen the brass disc from the hole in the steel plate, **cool down the system**.

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