C

To solve this problem, we need to analyze the forces acting on the blocks A, B, and C in relation to the applied external force F.
Step 1: Identify the mass of each block:
- Mass of A: 2 kg
- Mass of B: 3 kg
- Mass of C: 5 kg
Step 2: Calculate the maximum static friction force for each block. The static friction force can be calculated using the formula:
$$F_s = ext{friction}_{ ext{max}} = ext{friction coefficient} imes ext{normal force}$$
The normal force for each block is equal to their respective weights, where weight = mass * gravity (g = 9.8 m/s²). However, since the friction coefficient is not given, we will primarily focus on the given forces and check when relative motion occurs.
Step 3: Analyze the cases:
- For F = 13 N: This force is likely insufficient to overcome the friction between A and B, and B and C, leading to the conclusion that relative motion between A and B may occur, but without further information, we cannot definitively state about B and C. Therefore, this may correspond to [A].
- For F = 15 N: This force might just overcome the friction between B and C, leading to relative motion between B and C. This corresponds to [B].
- For F = 25 N: At this force, it might indicate sufficient force to create relative motion between C and the ground. Thus, it corresponds to [C].
- For F = 40 N: Since this force significantly exceeds the expected limits, relative motion is not present between any of the surfaces, leading to [D].
Summary: Based on the above analysis, the correct matching is:
(i) A; (ii) B; (iii) C; (iv) D.
Hence, the answer to the question 'match the entries' focusing on (iii) yields the correct answer as [C].