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Two identical blocks A and B each of mas...

Two identical blocks A and B each of mass M are connected to each other through a ligh 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.

Text Solution

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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 a=(F)/(2M))`
`(F)/(2)=F-T`

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

`T=(F)/(2)`
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