A particle is moving in a circle of radius R with constant speed v. The change in velocity when it moves from A to B sucb that `/_AOB=40^(@)` is

Options

A. `2vcos 20^(@)`
B. `2vsin 20^(@)`
C. `2vcos 40^(@)`
D. `2v sin 40^(@)`

Answer

B

Explanation

Change in velocity `Deltavecv=vecv_(2)-vecv_(1)=vecv_(2)+(-vecv_(1))`
`:.(Deltav)^(2)=v_(2)^(2)+v_(1)^(2)-2v_(1)v_(2)cos theta=v^(2)+v^(2)-2v^(2)cos theta `

`=2v^(2)(1-cos theta)=2v^(2)[1-1+2sin^(2)(theta//2)]=4v^(2)sin^(2)(theta//2)`
or `(Deltav)=2vsin(theta//2)=2vsin (40^(@)//2)=2vsin20^(@):.(Deltav)=2vsin 20^(@)`