In the arrangement shown in the figure pulleys are small, light and frictionless, threads are inextensible and mass of blocks `A`, `B` and `C` is `m_(1)=5kg`, `m_(2)=4kg` and `m_(3)=2.5kg` respectively and co-efficient of friction for both the planes is `mu=0.50`. Calculate the acceleration of block `A` (in `m//s^(2)`) when the system is released from rest. (`g=10 m//s^(2)`)

Answer

4

Explanation

With respect to the opening the height of the piston is 0.5m.
Pressure at the top is `P_(1)=P_(0)+(20xx10N)/(0.5m^(2))`
where `P_(0)` is the atmospheric pressure.
Pressure at the opening is `P_(2)=P_(0)`, From Bernoulli's equation, We have
`P_(1)+rhogh+(1)/(2)rhov_(1)^(2)=P_(2)+(1)/(2)rhov_(2)^(2)`
On solving, we get `v_(2)=3.3m//s=v_(x)` (say)
`v_(y)=sqrt(2gh)`
`v=sqrt(v_(x)^(2)+v_(y)^(2))=4.56 m//s`