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A rod AB of length 2m moves in horizonta...

A rod `AB` of length `2m` moves in horizontal `x-y` plane. At any instant end a of the rod is at origin and has velocity `vecv_(A)=2hati+v_(y)hatj`. The other end `B` at the same instant is moving with velocity `vecv_(B)=3hati+6hatj`. The rod makes an angle of `30^(@)` with the `x-`axis at this instant (see figure)
The magnitude of angular velocity of the rod is

A

`1 rad//sec`

B

`sqrt(3)rad//sec`

C

`(sqrt(3))/(2)rad//sec`

D

`1//2 rad//sec`

Text Solution

Verified by Experts

Unit vector along rod `hatl=(sqrt(3))/(2)hati+(1)/(2)hatj`
`hatlvecv_(1)=hatlvecv_(2)rArrv_(y)=(6+sqrt(3))m//s`
`omega=(|vecv_(2)-vecv_(1)|)/(l)=1 rad//sec`
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