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

Options

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))`

Answer

A

Explanation

Given, `T=30s, OQ=B`. The projection of the radius vector on the diameter of the circle when a particle is moving with uniform angular velocity `(omega)` on a circle of reference is SHM. Let the particle go from P to Q in time t.
Then `/_POQ=omegat=/_OQR`. The projection of radius OQ on x-axis will be `OR=x(t)` say.
In `DeltaOQR, sin omegat=(x(t))/(B)`
or `x(t)=Bsin omegat=Bsin((2pi)/(T))t=Bsin((2pi)/(30))t`