The system shown in fig, is released from rest. Calculate the tension in the string and the force exerted by the string on the pulleys, assuming pulleys and strings are massless.

Explanation

`T_(1) -lg =la"____"(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`
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