Two block of masses `m =5kg and M =10kg` are connected by a string passing over a pulley `B` as shown. Another string connect the center of pulley `B` to the floor and passes over another pulley `A` as shown. An upwards force `F` is applied at the center of pulley `A`. Both the pulleys are massless.
Find the acceleration of block `m` and `M`, if `F` is
(a) `100N`
`300N`
`500N(Take g = 10m//s^(2))`

Explanation

Let `T_(0) =` tension in the string passing over `A`
`T =` tension in the string passing over `B`
`2T_(0) =F` and `2T =T_(0)`
:. `T =F//4`
(a) `T =F//4 =25N`
weight of block are `mg =50N`
`mg =100N`
As `T lt mg ` and `Mg` both the block will remain stationary on the floor.
(b)`T =F//4 =75N`
As `T lt mg ` and `T gt mg,M` will remain stationary on the floor,whereas`m` will move.
Acceleration of `m`
`a =(T-mg)/(m) = (75-50)/(5)`
`= 5m//s^(2)`

(c) `T=F//4 =125N`
As `T gt mg `and `Mg` both the block will accelerate upwards
Acceleration of`m`,
`a =(T-mg)/(m) = (125-50)/(5)= 15m//s^(2)`
Acceleration of`M`,
`a =(T-Mg)/(M) = (125-100)/(10)= 2.5m//s^(2)`