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Question

A particle (P) is moving in a circle of radius (a) with a uniform speed (v). c is the center of the circle and AB is a diameter. The angular velocity of particle when it is at point B about (A) and (C) are in the ratio:

A
1:1
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B
1:2
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C
2:1
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D
4:1
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Solution

The correct option is B 1:2
The angular velocity of a particle about any point is given by:
ω=v/r ,
where, v= speed of particle
r= distance of particle from point
Here, given speed of particle is constant.
Angular speed about point A, ωA=v/AB=v/2a ( because AB=2a)
Angular speed about centre C, ωA=v/BC=v/a ( because BC=a)
Therefore, ωAωC=12

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