Question

For the given object and mirror arrangement, the velocity $($in $\text{cm/s})$ of the image with respect to ground will be
$[$All the velocities are given with respect to ground$]$

• A. $0$
• B. $2$
• C. $4$
• D. $6$

Answer 1

The correct option is A $0$

For the given convex mirror,
$u=-10\text{cm},f=+10\text{cm}$
Relative velocity of object with respect to mirror,
$v_{om}=v_{og}-v_{mg}=10-2=8\text{cm/s}$
Using mirror formula,
$\frac{1}{v}-\frac{1}{10}=\frac{1}{10}$
$\Rightarrow \frac{1}{v}=\frac{1}{5}$
$\Rightarrow v=5\text{cm}$
So, $m=\frac{-v}{u}=\frac{-5}{-10}=\frac{1}{2}$
Also, velocity of the image when the object is moving along the principal axis,
$v_{im}=-m^2{v}_{om}$
$\Rightarrow v_{im}=-{\left(\frac{1}{2}\right)}^2\times 8=-2\text{cm/s}$
Now, the velocity of the image with respect to ground,
$v_{ig}=v_{im}+v_{mg}$
$\Rightarrow v_{ig}=-2+2=0$

Why this question? It tests you on the application of the concept of image velocity and relative motion.