The system as shown in fig is released from rest. Calculate the tension in the strings and force exerted by the strings on the pulley. Assuming pulleys and strings are massless

Explanation

`T_(1)-1g=1a" ____(1)"`
`T_(2)-T_(1)=3a" ____(2)"`
`2g-T_(2)=2a" ____(3)"`
Solving the above equations,
we get, `a=(g)/(6)m//s^(2)`

`T_(1)=(7g)/(6)N, T+(2)=(5g)/(3)N`
Force on pulley `P_(1)` is `F_(1)=sqrt(T_(1)^(2)+T_(1)^(2))`
`=sqrt2T_(1)=(7g)/(3sqrt2)N`
Force on pulley `P_(2)` is `F_(2)=sqrt(T_(2)^(2)+T_(2)^(2))`
`=sqrt2T_(2)=(5sqrt2g)/(3)N`