Final answer:
The friction force between the 2 kg block A and the 8 kg block B, when a horizontal force is applied to block B, is 3.92 N, corresponding to option B, 3.9 N.
Step-by-step explanation:
To determine the friction force between block A (2 kg) and block B (8 kg) when a horizontal force is applied to block B, we need to consider the coefficient of friction and the normal force. Since the blocks remain together and the coefficient of friction between A and B is 0.2, we use the formula f = μN, where μ is the coefficient of friction and N is the normal force. The normal force on A is equal to its weight, which is mg, or 2 kg × 9.8 m/s² = 19.6 N. The maximum frictional force that can be exerted without sliding is thus 0.2 × 19.6 N = 3.92 N. Therefore, the friction force between the blocks A and B is 3.92 N, which is closest to the provided option B, 3.9 N.