The block `C` shown in the figure is ascending with an acceleration `a=3m//s^(2)` by means of some motor not shown here. Find the acceleration of the bodies `A` and `B` of masses `10 kg` and `5kg` respectively in `m//s^(2)`, assuming pulleys are massless and friction is absent everywhere.

Explanation

Drawing F.B.D. diagrams.

`10g-2T=10a_(A)` `(1)`
`5g-T=5a_(B)` `(2)`
`T` from equations `(1)` & `(2)` we get
`10a_(A)-10a_(B)=0`
`rArr a_(A)=a_(B)`
`l_(1)+l_(2)+l_(3)=`constant
`y_(E)+y_(A)+y_(A)+y_(B)=` costant
Differentiating twice w.r.t. time,
`a+2a_(A)+a_(B)=0`
`2a_(A)+a_(B)=-3`
or `3a_(0)= -3`
`rArr a_(B)=-1m//s^(2)`, `a_(A)=-1m//s^(2)`
`a_(A)=a_(B)=1m//s^(2)` upwards