Step 1: Understanding X-ray Diffraction Patterns.
X-ray diffraction (XRD) is a powerful technique used to analyze the structure of materials. When a material is irradiated with X-rays, the X-rays interact with the atomic planes in the material, causing diffraction. The diffraction pattern depends on the arrangement of atoms in the material. Crystalline materials typically exhibit distinct spot patterns, as the atomic planes are regularly spaced and oriented in a predictable manner. On the other hand, materials with isotropic structures (such as amorphous or unoriented materials) tend to produce patterns that are more diffuse and uniform.
Step 2: Isotropic Materials and Diffraction Patterns.
In the case of compression moulded isotropic polypropylene films, the polymer chains are oriented in a random fashion. This means the atomic planes are not aligned in a regular or periodic structure, as would be the case with crystalline materials. As a result, X-ray diffraction of isotropic materials typically produces a circular ring pattern. This pattern is indicative of the lack of long-range order in the material. The diffraction rings arise from the superposition of diffraction from many different crystal planes, each contributing to a part of the circular pattern.
Step 3: Analyzing the Options.
- (A) Spot pattern: This pattern is typical of crystalline materials with highly ordered atomic structures. Since polypropylene film is isotropic, it does not exhibit a spot pattern. Therefore, this option is incorrect.
- (B) Circular ring pattern: This is the correct answer. As explained earlier, isotropic polypropylene films exhibit circular rings in their diffraction patterns due to the random arrangement of polymer chains. This is a hallmark of materials that lack long-range order, like amorphous or isotropic substances.
- (C) Circular ring and spot pattern: This option suggests the presence of both a circular ring and a spot pattern. However, this is not typical of isotropic materials. The presence of both patterns would imply some degree of crystallinity, which is not the case for isotropic polypropylene. Therefore, this option is incorrect.
- (D) Arc pattern: An arc pattern would suggest some partial ordering or directional alignment in the material. Isotropic materials, by definition, do not show such partial alignments, so this option is also incorrect.
Step 4: Conclusion.
The correct answer is (B) circular ring pattern, as isotropic polypropylene films exhibit this type of diffraction pattern due to their lack of long-range atomic order.
Final Answer: \text{(B) circular ring pattern}
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).