A particle is moving along a circle with a uniform speed `v`. Find `(a)` change in the magnitude of velocity and `(b)` the magnitude of change in the velocity when it has rotated an angle `theta . (0 lt theta lt 90^(@))`

Options

A. `2v sin theta`
B. `2v sin (theta//2)`
C. `2v cos (theta//2)`
D. `sqrt2v cos (theta//2)`

Answer

B

Explanation

`|Delta vecv|=|vecv_(2) - vecv_(1)| = sqrt(v^(2) + v^(2) -2(v)(v) cos theta) `
`=sqrt(2v^(2) - 2v^(2) cos theta)`
`=sqrt(2v^(2) (1 - cos theta))`
`=sqrt(2v^(2)(2 sin^(2).(theta)/(2)))`
`= 2v sin.(theta)/(2)`