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If a particle rotates along a circle of ...

If a particle rotates along a circle of radius 3 m with an angular acceleration of `(pi)/(2) "rad"//s^(2)` starting from rest, then its average velocity over the time it covers quarter circle is :

A

`(pi)/(sqrt(2))m//s`

B

`(pi)/(2sqrt(2)) m//s`

C

`(2sqrt(2))/(pi)m//s`

D

`(pi)/(2) m//s`

Text Solution

Verified by Experts

The correct Answer is:
B
Let t be the time taken by the particle to go from A to B .

` :' theta = (1) /(2) alpha t^(2)`
` therefore (pi)/(2) =(1)/(2) xx(pi)/(4) xx t^(2) therefore t= 2s`
` V_(As) = ( "are" AB) /(t) =( r theta ) /(t) = ( sqrt(2 ) xxpi)/(2xx2) =(pi)/(2sqrt(2))m//s`
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