Four identical blocks, each of mass m, are connected as shown in and are kept on horizontal table. A force F is applied on the first block.Find the tension in each string, neglecting friction.

Explanation

Let the acceleration of the system, on the applying force F on the block, be a. let tension in the string connecting the 1 st and the 2nd block be `T_(1)`. 2nd and that for the 3rd be `T_(2)` and for the 3rd and the 4th be `T_(3)`
Equations of motion for the
1st block, F-`T_(1)`= ma ....(1)
2nd block, `T_(1) -T_(2)` = ma ...(2)
3rd block `T_(2) -T_(3)` = ma ...(3)
and 4th block, `T_(3)` = ma ...(4)
Since `T_(3)` = ma , `T_(2)` = ma + `T_(3)` = 2ma and `T_(1)` = 3ma.
Hence, applied force, f = ma + `T_(1)` = 4ma
Expressing the tensions in terms of the applied force f , we get
`T_(1) = (3)/(4)F, T_(2) = (F)/(2) and T_(3) = (F)/(4)`.