In a set of copolymerization reactions, the following monomer reactivity ratios (\(r_1\) and \(r_2\)) were found for different cases. 
Which option(s) correctly identify/identifies the type of copolymerization corresponding to each Case?
In this question, we need to analyze the given reactivity ratios (\(r_1\) and \(r_2\)) to determine the type of copolymerization for each case. The reactivity ratios tell us about the tendency of each monomer to react with the other. Based on these values, the following observations can be made:
- Ideal copolymerization (P): In ideal copolymerization, the monomer reactivity ratios \(r_1\) and \(r_2\) are typically close to each other, indicating that the monomers have similar tendencies to react with each other.
In Case I, we have \(r_1 = 0.1\) and \(r_2 = 10\), which shows a large disparity between the reactivity ratios. However, this does not imply extreme reactivity, suggesting that this case corresponds to ideal copolymerization.
- Azeotropic copolymerization (Q): Azeotropic copolymerization occurs when the reactivity ratios are both very low (less than 1), causing the copolymerization to proceed with little preference for one monomer over the other.
In Case II, the reactivity ratios \(r_1 = 0.003\) and \(r_2 = 0.02\) are very low, which is typical for azeotropic copolymerization.
- Block copolymerization (R): Block copolymerization occurs when one monomer has a significantly higher reactivity ratio compared to the other, resulting in the formation of distinct blocks of the monomers.
In Case III, \(r_1 = 3.4\) and \(r_2 = 5.6\), showing a relatively large disparity in the reactivity ratios, which is characteristic of block copolymerization.
Therefore, based on the given reactivity ratios, the correct answer is (A) P- Ideal copolymerization; Q- Azeotropic copolymerization; R- Block copolymerization.
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).