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 $9/\pi rps$. 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 incident becomes ${37}^{\circ }$, the speed of the spot (a point) on the wall is

• A. $10m{s}^{-1}$
• B. $1000m{s}^{-1}$
• C. $500m{s}^{-1}$
• D. None of these

Answer 1

The correct option is B $1000m{s}^{-1}$

When mirror is rotated with angular speed $\omega$, the reflected ray rotates with angular speed $2\omega (=36rad{s}^{-1})$
Speed of the spot $=\left|\frac{dh}{dt}\right|=\left|\frac{d}{dt}\right(10\cot \theta \left)\right|$
$=|-10cose{c}^2\theta \frac{d\theta }{dt}|=|-\frac{10}{(0.6{)}^2}\times 36|=1000m{s}^{-1}$.