A rotating mirror with uniform angular speed ω is placed at the centre (C) of the sphere of radius (R) as shown in the figure. Incident light falls on the mirror. The linear speed (v) of the light spot on the sphere is
A
ωR
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B
2ωR
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C
3ωR
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D
5ωR
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Solution
The correct option is B2ωR Given:
Angular speed of mirror =ω ⇒dθdt=ω
We know that the reflected ray gets rotated by two times of angle rotated by mirror. ⇒θR=2θ ⇒dθRdt=2dθdt ⇒ωR=2ω
Angular speed of reflected ray about centre of sphere, ωR=2ω
So, the linear speed of light spot will be, v=RωR=2ωR
Hence, option (b) is correct.