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Question

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 B 2ωR
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.

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