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In the circular motion of a particle. Th...

In the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. The simple harmonic motion of the x-projection of the radius vector of the rotating particle P is

A

`x (t) = B sin ((2pit)/(30))`

B

`x (t) = B cos ((pit)/(15))`

C

`x (t) = B sin ((pit)/(15) + (pi)/(2))`

D

`x(t) = B cos ((pit)/(15) + (pi)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the particle executing circular motion with angular velocity `omega` make an angle `theta` at P in time t.
So `theta = omegat` and T = 30 s
IN right angled triangle `angleOQP`,
`OQ = OP sin theta`
`x(t) = B sin omegat `
` = B sin (2pi)/(T)t`
` = B sin (2pi)/(30)t`
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