Question

A light ray `I` is incident on a plane mirror `M`.The mirror is rotated in the direction as shown in the figure by an arrow at frequency `(9)/(pi) "rev"//"sec"`,The light reflected by the mirror is received on the wall `W` at a distance `10m`from the axis of rotation .When the angle of incidence becomes `37^(@)`find the speed of the spot (a point) on the wall?

Answer 1

Correct Answer - `1000m//s`

`x=10 taxalpha`
`(dx)/(dt)=10 sec^(2) alpha(dalpha)/(dt)….(1)`
When mirror is rotaled by angle `theta` reflected ray will rotate by angle `2theta`,so
`(dalpha)/(dt)=2(d theta)/(dt)…..(2)`
From (1)&(2)
`(dx)/(dt)=10 sec^(2)alpha.2(d theta)/(dt) rArr (dx)/(dt)=20 sec^(2)alphaxxomega`
`(dx)/(dt)=20sec^(2)alphaxx2pi n rArr "when" i=37^(@),alpha=53^(@)`
`(dx)/(dt)=20sec^(2)53^(@)xx2pixx(9)/(pi) rArr (dx)/(dt)=20xx((5)/(3))^(2)xx2xx9`
`1000m//s`