
Figure shows a torch producing a straight light beam falling on a plane mirror at an angle . The reflected beam makes a spot P on the screen along the y-axis. If at the mirror starts rotating about the hinge A with an angular velocity clockwise, find the speed of the spot P on screen after .
A.
B.
C.
D.

Answer
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Hint: In order to find the speed of spot P, we will find the relation between the distance of spot on y-axis at time and when mirror rotates with angular velocity of then, the reflected ray from mirror will have the twice angular velocity and in time mirror will rotate by then the reflected ray will rotate by with the normal.
Complete step by step answer:
Let us first draw the diagram when after the reflected and incident ray will make an angle of so, from the geometry of figure we have, , let be the distance on y axis of spot denoted by .
In the right angle triangle we have,
Differentiate above equation with respect to time, we get
So we get,
Now as we know, is nothing but the velocity of spot lets denoted as . And since the angular velocity of mirror is the angular velocity of reflected ray will be and is nothing but this angular velocity which is
Converting into radian angle we have,
And, from the diagram we have, this
Put all the parameters value in equation we get,
............
Hence, the correct option is C.
Note:It must be remembered that, the angular speed at which mirror rotates, the reflected ray will rotate by twice the angle with which mirror rotate and hence twice the angular velocity of rotation of reflected ray, and angular velocity of the body is the differentiation of angular displacement with respect to time .
Complete step by step answer:
Let us first draw the diagram when after

In the right angle triangle
Differentiate above equation with respect to time, we get
So we get,
Now as we know,
Converting
And, from the diagram we have, this
Put all the parameters value in equation
Hence, the correct option is C.
Note:It must be remembered that, the angular speed at which mirror rotates, the reflected ray will rotate by twice the angle with which mirror rotate and hence twice the angular velocity of rotation of reflected ray, and angular velocity of the body is the differentiation of angular displacement with respect to time
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