Three blocks `m_(1), m_(2)`, and `m_(3)` are arranged as shown in fig. if `m_(2)=5 kg` and `m_(3)=8kg`, at what value of `m_(1)` will `8kg` mass be at rest?

Explanation

Here `T_(0)=8g=80N`
Also, `T_(0)=2T`
`:. T=40N`
From force diagram of 5 kg block,
`50-T=5a`
`50-40=5a`
`10=5a`
`a=2ms^(-2)`
From force diagram of `m_(1)`.
`T-m_(1)g=m_(1)a`
or `40-m_(1)g=m_(1) xx 2`
or `40 = 10m_(1)+2m_(1)=12m_(1)`
`:. m_(1)=40/12 = 10/3 kg`.