Figure shows a solid transport semi cylinder of radius `10 cm`. A screen is placed at a distance `60 cm` from `O`. A narrow beam is incident along `X-`axis at `O`. If cylinder starts rotating about `O` in clockwise direction with angular speed `6 rad//s` spot formed on screen will move upward (Refractive index of material of cylinder`=(5)/(3)`)

What is initial angular velcity of ray refrected from plane surface.

Options

A. `2 rad//s`
B. `10 rad//s`
C. `16 rad//s`
D. `4 rad//s`

Answer

D

Explanation

Angle of refracted ray from `x`-axis `theta=r-i`
For small angles
`r=mui`
`theta=(mu-1)irArr(d theta)/(dt)=(mu-1)(di)/(dt)=((5)/(3)-1)6=4 rad//s`