Question

Motion of a particle in $x - y$ plane is described by a set of following equations $x=4 \sin \left(\frac{\pi}{2}-\omega t\right) m$ and $y =4 \sin (\omega t ) m$. The path of particle will be $-$

• A. circular
• B. helical
• C. parabolic
• D. elliptical

Answer 1

Answer: (A)

$x=4 \sin \left(\frac{\pi}{2}-\omega t\right) y=4 \cos (\omega t) $
$x=4 \cos (\omega t) y=4 \sin (\omega t)$
Eliminate ' $t$ ' to find relation between $x$ and $y$
$x^{2}+y^{2}=y^{2} \cos ^{2} \omega t+y^{2} \sin ^{2} \omega t=4^{2}$
$x^{2}+y^{2}=4^{2}$