Question

A point object is placed at a distance of $30\text{cm}$ from the pole of a concave mirror on the principal axis. The velocity of the image with respect to ground will be,
$[$ The velocity of the object is given with respect to ground$]$

• A. $2\text{cm/s}$ downwards
• B. $2\text{cm/s}$ upwards
• C. $4\text{cm/s}$ upwards
• D. $4\text{cm/s}$ downwards

Answer 1

The correct option is D $4\text{cm/s}$ downwards

For the given concave mirror,
$u=-30\text{cm},f=-20\text{cm}$
Using mirror formula,
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\frac{1}{v}-\frac{1}{30}=\frac{-1}{20}$

After solving, we get,
$v=-60\text{cm}$
So, $m=\frac{-v}{u}=\frac{-(-60)}{-30}=-2$

Also, velocity of the image when the object is moving perpendicular to the principal axis, is given by,
$v_i=m{v}_o$
$\Rightarrow v_i=-2\times 2=-4\text{cm/s}$

Hence, $\left(D\right)$ is the correct answer.

Why this question? In such questions be cautious about the sign convention.