Question

The velocity of the image with respect to ground in the figure shown below figure will be :
$[$Mirror is at rest and velocity of the object $\left(O\right)$ is given with respect to ground$]$

• A. $45\text{m/s}$ towards the mirror
• B. $35\text{m/s}$ towards the mirror
• C. $45\text{m/s}$ away from the mirror
• D. $35\text{m/s}$ away from the mirror

Answer 1

The correct option is A $45\text{m/s}$ towards the mirror

For the given concave mirror,
$u=-20\text{cm},f=-30\text{cm}$
Using mirror formula,
$\frac{1}{v}-\frac{1}{20}=\frac{-1}{30}$
$\Rightarrow \frac{1}{v}=\frac{1}{60}$
$\Rightarrow v=60\text{cm}$
So, $m=\frac{-v}{u}=\frac{-60}{-20}=3$
Also, velocity of the image when the object is moving along the principal axis,
$v_{i,m}=-m^2{v}_{o,m}$
$\Rightarrow v_{i,m}=-(3{)}^2\times 5=-45\text{m/s}$
Since, the image is formed on the right side of the mirror $(v=+ve)$ and the image is moving in the left direction $(v_i=-ve)$, we can say that velocity of the image is towards the mirror.
Hence, the velocity of the image will be $45\text{m/s}$ towards the mirror.
$\begin{array}{c}\text{Why this question ?}\\ \text{Tips: When mirror is at rest, the velocity of}\\ \text{image w.r.t mirror will be same as velocity}\\ \text{of image w.r.t ground.}\end{array}$