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Wheel A of radius r(A)=10cm is coupled b...

Wheel `A` of radius `r_(A)=10cm` is coupled by a belt `C` to another wheel of radius `r_(B)=25 cm` as in the figure. The wheels are free to rotate and the belt does not slip . At time `t=0` wheel `A` increases it's angular speed from rest at a uniform rate `pi//2 rad //sec^(2)` Find the time in which wheel `B` attains a speed of `100 rpm [ ` Hint `: v_(A)=v_(B)]`

Text Solution

Verified by Experts

The correct Answer is:
`50//3 sec`.
For no slipping condition
`r_(A)alpha_(A)=r_(B)alpha_(B)`
`rArr alpha _(B)=(r_(A))/(r_(B))alpha_(A)=(10)/(25)xx(pi)/(2)=(pi)/(5) rad //s^(2)`
`omega_(B)=(2pixx100)/(60)=(10pi)/(3)rad//s`
`omega_(B)=omega_(BO)+alpha_(B)t`
`(10pi)/(3)=0+(pi)/(5)trArr t=(50)/(3)sec`
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