A particle moving with a speed v changes direction by an angle `theta`, without change in speed.

Options

A. (a)The change in the magnitude of its velocity is zero
B. (b)The change in the magnitude of its velocity is The magnitude of the change in its velocity is 2 v sin `(theta//2)`
C. (c)The magnitude of the change in its velocity is `v(1-costheta)`
D. (d)The magnitude of the change in its velocity is 2v sin (θ/2)

Answer

A, C

Explanation

`overset(-)v_(1)=v hati, overset(-)v_(f)=V cos theta hati+V sin theta hatj rArr triangle overset(-)(V)=(V cos theta-v)hati+v sin theta hatj`
`|triangle overset(-)v|=sqrt(v^(2) cos^(2) theta+v^(2)-2v^(2) cos theta+v^(2) sin^(2) theta)`
`=sqrt(2v^(2)-2v^(2) cos^(2) theta) =2v sin (theta//2)`