Question

The radius of circle, period of revolution, initial position and sense of revolution are indicated in the figure.


The y-projection of the radius vector of the rotating particle $P$ is

• A. $y\left(t\right)=-3\cos 2\pi t$, where $y$ is in $m$
• B. $y\left(t\right)=4\sin \left(\frac{\pi t}{2}\right)$, where $y$ is in $m$
• C. $y\left(t\right)=3\cos \left(\frac{3\pi t}{2}\right)$, where $y$ is in $m$
• D. $y\left(t\right)=3\cos \left(\frac{\pi t}{2}\right)$, where $y$ is in $m$

Answer 1

The correct option is D $y\left(t\right)=3\cos \left(\frac{\pi t}{2}\right)$, where $y$ is in $m$


$\omega =\frac{2\pi }{T}=\frac{2\pi }{4}=\frac{\pi }{2}$
As the particle is rotating in XY-Plane, its projection on Y-axis represents simple harmonic motion with an amplitude of 3 $m$
$y=A\cos \left(\omega t\right)\Rightarrow y=3\cos \left(\frac{\pi t}{2}\right)$