Calculate the acceleration .a. of the system and the tensions `T_(1) and T_(2)` in the strings as shown in figure. (Assume that the table and the pulleys are frictionless and the string is massless and in-extensible).

Explanation

Net force on box of 5 kg
`" "5g-T_(2)=5 times a" …(1)"`
Net force on box of 10 kg
`" "T_(2)-T_(1)=10 times a" …(2)"`
Net force on box of 3 kg
`" "T_(1)-3g=3a" …(3)"`
adding equations (1) and (2) we get
`" "5g-T_(1)=15a" ...(4)"`
`" "T_(1)-3g=3a" ...(3)"`
adding equations (3) and (4) we get
`" "2g=18a`
`" "a=(2 times 9.8)/(18)=(9.8)/9=1.08m//sec^(2)`
`" "a=1.08m//sec^(2)`
From equation (3)
`" "T_(1)=3a+3g=3 times 1.08 +3 times 9.8`
`" "=3.24+39.4`
`" "T_(1)=32.64N`
From equation (1),
`" "T_(2)=5g-5a`
`" "T_(2)=5 times 9.8-5 times 1.08`
`" "T_(2)=49-5.4`
`" "T_(2)=43.6N`