question_answer

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 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) None of these

Correct Answer: B

Solution :

[b] When mirror is rotated with angular speed \[{{N}_{1}}\times \frac{\ell }{4}={{N}_{2}}\times \frac{\ell }{3}\] the reflected ray rotates with angular speed \[2\,\omega =(36\,rad/s)\] sped of spot \[=\left| \frac{dh}{dt} \right|=\left| \frac{d}{dt}(10\,\cot \theta ) \right|=\left| -\,10\,\text{cose}{{\text{c}}^{2}}\theta \,\frac{d\theta }{dt} \right|\] \[=\,\left| -\frac{10}{{{(0.6)}^{2}}}\times 36 \right|=\,1000\,m/s\].