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 freuqency `9//pi` rps. The light reflected by the mirror is received on the wall W at a distance 10 m from the axis of rotation. When the angle of incidence becomes `37^(@)`, the speed of the sopt (a point) on the wall is

Options

A. 10 m/s
B. 1000 m/s
C. 360 m/s
D. None of these

Answer

B

Explanation

As we know the `omega_("reflected ray") = 2 omega_("mirror")`
`omega_(R)= 2 xx 2pi xx (9)/(pi)= 18 xx 2 = 36 therefore v_(S) "cos"37^(@) = v`
`v_(S) = v"sec" 53^(@) = Romega_(R)"sec"53^(@) = 10 ("sec"53^(@))^(2) xx 18`
=` 10 xx ((5)/(3))^(2) xx 18 xx 2 = 1000 "m"//"s"`