Question

A particle moves in a circle of radius $2\text{cm}$ with a constant angular velocity. A concave mirror of focal length $20\text{cm}$ is placed with its principal axis passing through the center of the circle and perpendicular to its plane. The distance between the pole of the mirror and the center of the circle is $30\text{cm}$. The ratio of acceleration of image to that of object is

Answer 1

$\left|\begin{array}{c}m\end{array}\right|=\left|\begin{array}{c}\frac{f}{f-u}\end{array}\right|=\left|\begin{array}{c}\frac{-20}{-20+30}\end{array}\right|=2$


$\because m=\frac{r_I}{r_O}$

$r_O=2\text{cm}$

$\therefore r_I=m{r}_O=4\text{cm}$

Angular velocity is same and constant.

So, $\frac{a_I}{a_O}=\frac{r_I}{r_O}=2$