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 $\frac{9}{\pi }$ 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 ${37}^{\circ }$, the speed of the spot (a point) on the wall is

• A. 10 m/s
• B. 1000 m/s
• C. 500 m/s
• D. 20 m/s

Answer 1

The correct option is C

500 m/s

$y=10cot\theta$

$(-\frac{dy}{dt})=\left(10cose{c}^2\theta \right)\left(\frac{d\theta }{dt}\right)$

$\therefore v_p=\left(10cose{c}^2\theta \right)\omega$

$=\left(2\pi f\right)\left(10cose{c}^2{37}^{\circ }\right)$

$=\left(2\right)\left(\pi \right)\left(\frac{9}{\pi }\right)\left(10\right)\left(\frac{25}{9}\right)=500m/s$