Step 1: Analyze the options.
(A) Polyamide 6,6: Polyamide 6,6, also known as nylon 6,6, is a type of thermoplastic, not an elastomer. It is used in textiles and engineering plastics, but it does not exhibit the elastic properties characteristic of elastomers.
(B) Poly(ethylene terephthalate): Poly(ethylene terephthalate) (PET) is commonly used in fibers and containers. PET is a rigid plastic and does not show the elasticity needed for an elastomer.
(C) Vulcanized polybutadiene: Vulcanized polybutadiene is a well-known elastomer. The vulcanization process enhances the elasticity of the material, making it ideal for use in tires and various rubber products.
(D) High density polyethylene: High density polyethylene (HDPE) is a thermoplastic polymer, known for its strength and rigidity. It does not possess the elasticity required to be classified as an elastomer.
Step 2: Conclusion.
The correct answer is (C) Vulcanized polybutadiene, which is an elastomer due to its excellent elastic properties.
Final Answer: (C) Vulcanized polybutadiene
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 \(\underline{\hspace{2cm}}\).
Potato slices weighing 50 kg is dried from 60% moisture content (wet basis) to 5% moisture content (dry basis). The amount of dried potato slices obtained (in kg) is ............ (Answer in integer)
Two Carnot heat engines (E1 and E2) are operating in series as shown in the figure. Engine E1 receives heat from a reservoir at \(T_H = 1600 \, {K}\) and does work \(W_1\). Engine E2 receives heat from an intermediate reservoir at \(T\), does work \(W_2\), and rejects heat to a reservoir at \(T_L = 400 \, {K}\). Both the engines have identical thermal efficiencies. The temperature \(T\) (in K) of the intermediate reservoir is ........ (answer in integer). 
A bar of length \( L = 1 \, {m} \) is fixed at one end. Before heating its free end has a gap of \( \delta = 0.1 \, {mm} \) from a rigid wall as shown in the figure. Now the bar is heated resulting in a uniform temperature rise of \( 10^\circ {C} \). The coefficient of linear thermal expansion of the material is \( 20 \times 10^{-6} / \degree C \) and the Young’s modulus of elasticity is 100 GPa. Assume that the material properties do not change with temperature.
The magnitude of the resulting axial stress on the bar is .......... MPa (in integer). 
A massless cantilever beam, with a tip mass \( m \) of 10 kg, is modeled as an equivalent spring-mass system as shown in the figure. The beam is of length \( L = 1 \, {m} \), with a circular cross-section of diameter \( d = 20 \, {mm} \). The Young’s modulus of the beam material is 200 GPa.
The natural frequency of the spring-mass system is ............ Hz (rounded off to two decimal places).
A simply-supported beam has a circular cross-section with a diameter of 20 mm, area of 314.2 mm\(^2\), area moment of inertia of 7854 mm\(^4\), and a length \( L \) of 4 m. A point load \( P = 100 \, {N} \) acts at the center and an axial load \( Q = 20 \, {kN} \) acts through the centroidal axis as shown in the figure.
The magnitude of the offset between the neutral axis and the centroidal axis, at \( L/2 \) from the left, is ............ mm (rounded off to one decimal place).