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

Explanation

a) In this case net pulling force
`=m_(A)g sin 60^(@)+m_(B)g sin 60^(@)-m_(C )g sin 30^(@)`
`=(1)(10)(sqrt3)/(2)+(3)(10)((sqrt3)/(2))-(2)(10)((1)/(2))=24.64N`
`"Total mass "=1+3+2=6kg`
`therefore" Acceleration of the system"`
`a=(24.64)/(6)=4.1m//s^(2)`
b) For the tension in the string between A and B.
FBD of Body A

`m_(A)g sin 60-T_(1)=m_(A)a`
`T_(1)=m_(A)g sin 60-m_(A)a=m_(A)(g sin 60-a)`
`T_(1)=(1)(10xx(sqrt3)/(2)-4.1)=4.56N`
For the tension in the string between B and C FBD of body C

`T_(2)=m_(C)g sin 30^(@)=m_(C)a, T_(2)=m_(C)(g sin theta 30^(@)+a)`
`T_(2)=2(10((1)/(2))+4.1)=18.2N`