A 4 kg block A is placed at the top of 8 kg block B which rests on a smooth table. A just slips on B when a force of 20 N is applied on A. The maximum horizontal force F required to make both A & B move together is

Given:

Mass of block A = 4 kg

Mass of block B = 8 kg

Force required to make A slip on B = 20 N (This is the maximum friction force between the two blocks)

Since the force required to make A slip is 20 N, the maximum static friction force is 20 N.

Total mass of both blocks = 4 kg + 8 kg = 12 kg

To ensure both blocks move together, friction must provide sufficient force to prevent slipping. From Newton's second law:

Friction force 

Since f_max =20 N,

m_A×a = 20

From this,

a= 4/20 =5 m/s²

Now calculate the total force required to achieve this acceleration:

F=m _total × a=12×5 = 60N