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Question

A ray of light I is incident on a plane mirror M. The mirror is rotated in the direction as shown in the figure by an arrow at frequency 18π cps. The light reflected by the mirror is received on the wall W at a distance 10m from the axis of rotation. When the angle of incidence becomes 3? the speed of the spot (a point) on the wall is
1276743_3160c68f64444c37a2e1f240ec34bd5b.PNG

A
100m/s
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B
1000m/s
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C
2000m/s
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D
500m/s
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Solution

The correct option is C 2000m/s
assume incidence angle i 37
α=9037=53
take Q= angle of rotationtion of mirror α=2θ
We have to find
speed to point P ie dxdt
change in x wir.t
time.
as image is ratated
twice the angle in which
mirror rotates. [dαdt2dQdt]
how, tanα=x10x=40tanα
dxdt=10sec2αdαd+,dxdt=20sec2αdQdtdQdt=ω=2πf20sec2αωω20sec2α(2π(18π))
dxd+=40×(53)2×18720×259
2000 m/s
: speed of point p is 2000 m/s
Hence option (c) matenes.

2001921_1276743_ans_fa79b323e4f6420ea986b9201594d525.PNG

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