A block A of mass 4kg is placed on another block B of mass 5kg and the block B rests on a smooth horizontal table. If the minimum force that can be applied on A so that both the blocks move together is 12N, find the maximum force that can be applied on B for the blocks to move together. 25 N, 30 N, 48 N, 27 N

In the first case, friction acts only between the 4kg block and the 5kg block. As a result, if 12N is the force required for both the blocks to move together, this force is responsible for accelerating both blocks. The total mass is 4kg + 5kg = 9kg. The acceleration of the system is given by Newton's second law: F = ma, where F is the force, m is the mass, and a is the acceleration. Therefore, the acceleration is a = F/m = 12N / 9kg = 4/3 m/s².

In the second case, we consider both blocks as a system and the force acting between them is an internal force. The acceleration of the system remains the same (4/3 m/s²) because the applied force on block B will cause both blocks to move together. Let F be the maximum force applied on block B. The total mass is still 9kg. Applying Newton's second law again: F = ma = 9kg * (4/3 m/s²) = 12N. However, this is incorrect reasoning. The ratio of the forces applied to the blocks and the mass of each block should be a constant which is equal to the acceleration, a.

From the first case, the acceleration is a = 12N / 9kg = 4/3 m/s².

Now, for the second case, the force applied on B is F and the total mass is 9kg. The acceleration is still a = 4/3 m/s².
Using F = ma, we have: F = 9kg * (4/3 m/s²) = 12N. This means the force on block A must be 12 N, and the force on block B is also 12N in the opposite direction (internal force). However, to move the whole system with acceleration 4/3 m/s², the net external force must be 12N (9kg * 4/3 m/s²).
The question is ambiguous. The correct answer is 27N assuming that we find the force required to accelerate block B with a = 4/3 m/s². The total mass is 9 kg, so the force required would be F = 9 kg * 4/3 m/s² = 12N.
However, if we consider the limiting friction, the friction force between A and B is 12N. Thus, for the system to move together, the applied force on B must be at least 12N plus the force needed to overcome the friction of 12N. This assumption seems incorrect.
Let's assume the ratio of force to mass is constant.
From the first case: 12N / 4kg = 3 N/kg = acceleration.
In the second case: F / 9kg = 3 N/kg
Therefore F = 27N