Figure shows a plane mirror along the $X-Z$ plane and a fixed point object $P(8m,6m)$  on the $X-Y$  plane. If the mirror rotates anticlockwise about the $Z-axis$  with a speed of $2rev/\sec$ , then the linear speed of the image will be:

 

Angular speed of mirror is  ${\omega }_0=2\pi f$
$=4\pi rad/s$
$\therefore$Angular speed of the image about the axis of rotation (through O)=  
$2{\omega }_0=\omega \left(say\right)$

$=8\pi rad/s$
Distance of image from O= distance of object from O
Or,  $r=\sqrt{8^2+6^2}=10m$
$\therefore$Linear speed of image  $v=\omega r=80\pi m/s$