Question

For the arrangement shown in the figure. The velocity of image with respect to ground will be:
$[$All the velocities are given with respect to ground$]$

• A. $2\text{cm/s}$ in $+y$ direction
• B. $2\text{cm/s}$ in $-y$ direction
• C. $4\text{cm/s}$ in $+y$ direction
• D. $4\text{cm/s}$ in $-y$ direction

Answer 1

The correct option is A $2\text{cm/s}$ in $+y$ direction

For the given concave mirror,
$u=-30\text{cm},f=-20\text{cm}$
Relative velocity of object with respect to mirror in perpendicular to the principal axis,
$v_{om}=v_{og}-v_{mg}=2-2=0$
Also, velocity of the image when the object is moving perpendicular to the principal axis,
$v_{im}=m{v}_{om}$
$\Rightarrow v_{im}=0$
Now, the velocity of the image with respect to ground,
$v_{ig}=v_{im}+v_{mg}$
$\Rightarrow v_{ig}=0+2=2\text{cm/s}$
Hence, the velocity of the image with respect to ground will be $2\text{cm/s}$ in $+y$ direction.

$\text{Why this question?}$ $\text{Caution: In excitement you may mark 'zero' as image velocity. Always remember about which respect the image velocity has been asked.}$