A wheel `A` is connected to a second wheel `B` by means of in extensible string, passing over a pulley `C`, which rotates about a fixed horizontal axle `O`, as shown in the figure. The system is released from rest. The wheel `A` rolls down the inclined plane `OK` thus pulling up wheel `B` which rolls along the inclined plane `ON`.

Determine the velocity (in m/s) of the axle of wheel `A`, when it has traveled a distance `s = 3.5 m` down the to be slope. Both wheels and the pulley are assumed homogeneous disks of identical weight and radius. Neglect the weight of the string. The string does not slip over `C`. [Take `alpha =53^@` and `beta=37^@`]

Answer

2

Explanation

Applying conservation of energy
`mgs(sin alpha-sin beta)=1/2 I omega^(2)+2(1/2 mv^(2)+1/2 I omega^(2))`
where `omega=v//r` & `I=mr^(2)//2`
Putting values & solving
`mgs(sin alpha- sin beta)=7/4 mv^(2)`
`:.v=2sqrt(1/7 gs (sin alpha-sin beta))`
`=sqrt(10xx3.5/7(4/5-3/5))=2m//s`