In the adjacent figure, masses of `A,B` and `C` are `1kg ,3kg` and `2kg` respectively.Find
(a) the acceleration of the system and
(b) tension in the strings.
Neglect friction.`(g=10m//s^(2))`

Explanation

In this case net pulling force
`=m_(A)g sin 60^(0) + m_(B) g sin 60^(0) -m_(C)g sin 30^(0)`
`= (1) (10) (sqrt3)/(2) + (3) (10) ((sqrt3)/(2))-(2) (10) ((1)/(2))=24.64N`
Total mass `=1 +3 +2 =6kg`
`:.` Acceleration of the system
`a =(24.64)/(6) =4.1m//s^(2)`
(b) For the tension the string between `A` and `B`.
`FBD` of body `A`
`m_(A)g sin 60 -T_(1) =m_(A)a`
`T_(1) =m_(A) sin 60 -m_(A) a =m_(A)(g sin 60-a)`
`T_(1) =(1) (10xx(sqrt3)/(2)-4.1)=4.56N`
For the tension the string between `B` and `C` `FBD` of body `C`
`T_(2) -m_(C)g sin 30^(0) =m_(C) a, T_(2) =m_(C) (g sin 30^(0) +a)`
`T_(2) =2 (10((1)/(2))+4.1)=18.2N`

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