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The steel balls A and B have a mass of 5...

The steel balls `A` and `B` have a mass of `500 g` each and al rotating about the vertical axis with an angular velocity of `4 rad//s` at a distance of `15 CM` from the axis. Collar `C` is now forced down until the balls are at a distance `5 CM` from the axis. How Much work must be done move the collar down?

Text Solution

Verified by Experts

In process angular momentum remains constant
`I_(1)omega_(1)=I_(2)omega_(2)`
Where `I_(1)=2m(0.15)^(2), omega_(1)=4rad//s`
`I_(2)=2m(0.05)^(2)`
Substituting these values in above equation, we get
`omega_(2)=(I_(1)omega_(1))/I_(2)=36rad//s`
Work done on the collar
`W=1/2I_(2)omega_(2)^(2)-1/2I_(1)omega_(1)^(2)`
or `W=1/2(0.05)^(2)xx36^(2)-1/2 2m(0.015)^(2)xx4^(2)`
where `m=500/1000=0.05kg=1.44J`
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