STATEMENT - 1 : A metallic rod is clamped between two fixed support. The rod is heated but not allowed to bend. Tensile stress is developed in it.
STATEMENT - 2 : A metallic rod is fixed between two rigid supports. The rod is heated. The strain produced in the rod is ZERO because there is no change in length
STATEMENT - 3 : The practical value of Poisson's ratio lies between 0 and 0.5.

Options

A. a. TTT
B. b. FTF
C. c. FFT
D. d. FFF

Answer

To analyze the statements provided in the question, we will evaluate each statement one by one.

### Step 1: Evaluate Statement 1
**Statement 1**: A metallic rod is clamped between two fixed supports. The rod is heated but not allowed to bend. Tensile stress is developed in it.

- When a metallic rod is heated, it tends to expand. However, since it is clamped between two fixed supports, this expansion is restricted.
- The restriction prevents the rod from expanding freely, which creates internal stresses in the material.
- Since the rod cannot expand, it develops tensile stress as it tries to elongate but is held back by the supports.

**Conclusion**: Statement 1 is **True**.

### Step 2: Evaluate Statement 2
**Statement 2**: A metallic rod is fixed between two rigid supports. The rod is heated. The strain produced in the rod is ZERO because there is no change in length.

- When the rod is heated, it attempts to expand. However, because it is fixed at both ends, it cannot change its length.
- The rod experiences internal stresses due to the restriction of its thermal expansion, but since it cannot change its length, the strain is effectively zero.

**Conclusion**: Statement 2 is **True**.

### Step 3: Evaluate Statement 3
**Statement 3**: The practical value of Poisson's ratio lies between 0 and 0.5.

- Poisson's ratio (ν) is defined as the ratio of transverse strain to axial strain when a material is deformed elastically.
- For most materials, the value of Poisson's ratio typically ranges from 0 to 0.5. A value of 0.5 indicates that the material is incompressible, while 0 indicates that there is no lateral expansion when stretched.
- Therefore, the practical value of Poisson's ratio does indeed lie between 0 and 0.5.

**Conclusion**: Statement 3 is **True**.

### Final Conclusion
All three statements are true. Therefore, the correct answer is that all statements are valid.

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