Question

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

• A. $10\text{m/s}$ moving downwards
• B. $20\text{m/s}$ moving downwards
• C. $20\text{m/s}$ moving upwards
• D. $10\text{m/s}$ moving upwards

Answer 1

The correct option is A $10\text{m/s}$ moving downwards

For the given concave mirror,
$u=-30\text{cm},f=-20\text{cm}$
Using mirror formula,
$\frac{1}{v}-\frac{1}{30}=\frac{-1}{20}$
$\Rightarrow \frac{1}{v}=\frac{-1}{60}$
$\Rightarrow v=-60\text{cm}$
So, $m=\frac{-v}{u}=\frac{-(-60)}{-30}=-2$
Also, velocity of the image when the object is moving perpendicular to the principal axis,
$v_{i,m}=m{v}_{o,m}$
$\Rightarrow v_{i,m}=-2\times 5=-10\text{m/s}$
Hence, the velocity of the image will be $10\text{m/s}$ downwards.
$\begin{array}{c}\text{Why this question ?}\\ \text{Tips: When the object is moving}\perp \text{to principal}\\ \text{axis, image velocity formula is valid for point}\\ \text{object only.}\\ \text{Caution: Downward direction of velocity w.r.t}\\ \text{principal axis is taken negative.}\end{array}$