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Question

A particle is moving uniformly in a circular path of radius 10 m. When it moves through a displacement 5 m, then the magnitude of the corresponding angular displacement will be:

A
20o
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B
30o
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C
600
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D
90o
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Solution

The correct option is C 600
In the figure, the angle AOB is equal to θ.
The liner displacement corresponding to the angular displacement θ is AB.
We know AB = 5 m and r = 10 m
Let C be the mid point of AB. Hence the angle COB is θ/2.
Since OBC forms a right angle triangle, BC=rsin(θ2)
Hence AB=2BC=2rsin(θ2)
θ = 2×sin1(AB2r)
θ = 2×sin1(52×5)
θ = 2×30
θ = 60

612654_573493_ans_4ccfb78970d44fa5a7f68140c366c9fb.png

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