Two identical blocks A and B each of mass M are connected to each other through a light string. The system is placed on a smooth horizontal floor. When a constant force F is applied horizontally on the block A, find the tension in the string.

Explanation

The acceleration of the system of two blocks A and `B=("Force")/("Total mass")`
`therefore a=F/(M+M) =F/(2M)`
If we consider the free body diagram of A, the forces acting on it are
(i) the applied force F and
(ii) the tension T on the string as shown in the following fig.

The resultant force F-T, Ma =F-T
`M(F/(2M)) = F-T (therefore =F/(2M))`
`F/2 =F-T`

`T=F/2` (or) From FBD for B

`T= Ma = MF/(2M) =F/2, T=F/2`