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**Hint:**In order to solve this question, we will use the concept that whenever a plane mirror rotates to an angle say $\theta $ then the light ray which is reflected from the plane mirror will rotate through an angle of $2\theta $ and hence will make double rotations as compared with rotations of plane mirror.

**Complete answer:**

As, it’s given that the plane mirror rotates with the number of revolutions in one second is $12$ .

So, the number of revolutions made by reflected rays from the plane mirror will be twice of twelve which is $24$ .

Also, this number of revolutions per second is also called the frequency of the body so, $f = 24$

Speed of the reflected light can be calculated by:

$v = 2\pi R \times f$

Where, $R = 1.5m$ which is the radius of the sphere.

So,

$v = 2\pi \times 1.5 \times 24$

$v = 72\pi m{\sec ^{ - 1}}$

Hence, the speed of the light spot on the surface is given by $v = 72\pi m{\sec ^{ - 1}}$ .

**Note:**It must be remembered that, whenever a plane mirror is rotated with some angle say $\theta $ then the reflected ray of light will always rotate with an angle of $2\theta $ and the revolutions per second is the frequency of a body in $radians{\sec ^{ - 1}}$ , which also have a unit denoted as $Hertz$ written as $Hz$.

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