Question

Equal and opposite forces of a constant magnitude \( F \) are applied at the two ends of a thin elastomeric rod, which is held at a temperature \( T_1 \) (where \( T_g < T_1 < T_m \), and \( T_g \) and \( T_m \) are the glass transition temperature and melting temperature respectively). If the temperature is increased to \( T_2 \) (where \( T_g < T_2 < T_m \) and \( T_2 > T_1 \)), the rod will \(\underline{\hspace{2cm}}\).

• A. expand along the loading direction and the transverse direction
• B. shrink along the loading direction
• C. remain dimensionally unaltered
• D. expand only along the loading direction

Hint:

Elastomeric materials behave differently above and below their glass transition temperature. Between \( T_g \) and \( T_m \), they become more flexible and can shrink under applied forces.

Answer 1

The Correct Option is B

Step 1: Understand the behavior of the elastomeric rod at different temperatures.
The elastomeric material has different behaviors in different temperature ranges. Below the glass transition temperature (\( T_g \)), the polymer chains are rigid, and the material shows limited movement. When the temperature is raised to a point between \( T_g \) and \( T_m \), the material becomes more flexible and behaves differently under applied stress.

Step 2: Impact of increased temperature on the rod.
As the temperature increases from \( T_1 \) to \( T_2 \), the polymer becomes more flexible. In this range of temperatures, the rod will shrink along the loading direction due to the softening of the material and will not expand in the transverse direction.

Step 3: Conclusion.
Thus, the rod will shrink along the loading direction when the temperature increases from \( T_1 \) to \( T_2 \), making option (B) the correct choice.

Final Answer: (B) shrink along the loading direction