A particle is moving an a cirle of radius 'r' and centre O with constant speed . What is the change in velocity in moving from A to B ?
(If any angle between two velocity vector is `theta`.)

Options

A. `2v sin ^(2)theta//2`
B. `2v sin theta//2`
C. `2v sin ^(2) theta//2`
D. `2v cos theta//2`

Answer

B

Explanation

`Here|vecv_(A)|=|vecv_(B)|=v`

change in velocity
`Delta vec v=vecv_(B)-vecv_(A)`
`=v_(B)+(-vecv_(A))`
The angle between `vec v _(A) is =180-theta`
`therefore |vec Delta v|=sqrt(v_(A)^(2)+v_(B)^(2)+2v_(A)v_(B) cos (180-theta))`
`Delta v =sqrt(v^(2)+v^(2)-2v^(2) cos theta)`
`=vsqrt(2-2 cos theta)`
`=vsqrt(2(1- cos theta))`
`=vsqrt(2xx2 sin ^(2))(theta)/(2)=2v "sin"(theta)/(2)`
`v=omega r.`