Introduction:
In this problem, we have two blocks A and B placed in contact on a smooth horizontal surface. A force of 100 Newton is acting on both blocks. We need to find the magnitude of the force which block A exerts on block B.

Analysis:
To solve this problem, we need to understand the concept of Newton's third law of motion which states that for every action, there is an equal and opposite reaction. In this case, the force of 100 Newton acting on both blocks is the action force. According to Newton's third law, block A will exert an equal and opposite reaction force on block B.

Calculation:
To calculate the magnitude of the force which block A exerts on block B, we can use the formula:

Force = mass * acceleration

Since the blocks are in contact and on a smooth horizontal surface, the acceleration of both blocks will be the same. Let's assume the acceleration to be 'a'.

For block A:
Force(A) = mass(A) * acceleration = 2 kg * a

For block B:
Force(B) = mass(B) * acceleration = 3 kg * a

According to Newton's third law, the force exerted by block A on block B will be equal in magnitude but opposite in direction to the force exerted by block B on block A. Therefore, we can write:

Force(A on B) = Force(B on A)

2 kg * a = 3 kg * a

Simplifying the equation, we get:

2a = 3a

a cancels out from both sides, leaving us with:

2 = 3

This is not possible, which means our assumption of equal acceleration for both blocks is incorrect. Since the blocks are on a smooth horizontal surface, there is no friction between them. Therefore, the force exerted by block A on block B will be zero.