A disc of radius `R` rolls without slipping at speed `v` along positive `x`-axis. Velocity of point `P` at the instant shown in Fig. is

Options

A. `vecV_(P)=(v+(vrsintheta)/R)hati+(vrcostheta)/Rhatj`
B. `vecV_(P)=(v+(vrsintheta)/R)hati-(vrcostheta)/Rhatj`
C. `vecV_(P)=(vrsintheta)/Rhati+(vrcostheta)/Rhatj`
D. `vecV_(P)=(vrsitheta)/R hati-(vrcostheta)/Rhatj`

Answer

B

Explanation

Here `omega=v/R`
`v_(P_x)=(v+v/R rsintheta)hati`
`V_(P_(y))=(v/R r costheta)hatj`
`:. vecV_(P)=(v+(vrsintheta)/R)hati-(vrcosrtheta)/Rhatj`
`=(v+(vrsitheta)/r)hati-(vrcostheta)/Rhatj`