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))

In the adjacent fig, masses of A, B and C are 1 kg, 3kg and 2kg respec

1.	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))
Answer» Solution :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`