Question

A rotating mirror with uniform angular speed $\omega$ is placed at the centre $\left(C\right)$ of the sphere of radius $\left(R\right)$ as shown in the figure. Incident light falls on the mirror. The linear speed $\left(v\right)$ of the light spot on the sphere is

• A. $\omega R$
• B. $2\omega R$
• C. $3\omega R$
• D. $5\omega R$

Answer 1

The correct option is B $2\omega R$

Given:
Angular speed of mirror $=\omega$
$\Rightarrow \frac{d\theta }{dt}=\omega$
We know that the reflected ray gets rotated by two times of angle rotated by mirror.
$\Rightarrow {\theta }_R=2\theta$
$\Rightarrow \frac{d{\theta }_R}{dt}=\frac{2d\theta }{dt}$
$\Rightarrow {\omega }_R=2\omega$
Angular speed of reflected ray about centre of sphere, ${\omega }_R=2\omega$
So, the linear speed of light spot will be,
$v=R{\omega }_R=2\omega R$
Hence, option $\left(b\right)$ is correct.