Previous Year NEET Question- Optics L-10

Question: A particle moves in $x-y$ plane according to rule $x=a \sin \omega t$ and $y=a \cos \omega t$. The particle follows#

A) an elliptical path

B) a circular path

C) a parabolic path

D) a straight line path inclined equally to $x$ and $y$-axes

Answer: a circular path#

Sol:#

$x=a \sin \omega t$ or $\frac{x}{a}=\sin \omega t$ $y=a \cos \omega t$ or $\frac{y}{a}=\cos \omega t$

Squaring and adding, we get $$ \begin{aligned} & \frac{x^2}{a^2}+\frac{y^2}{a^2}=1 \quad\left(\therefore \cos ^2 \omega t+\sin ^2 \omega t=1\right) \ & \text { or } x^2+y^2=a^2 \end{aligned} $$

This is the equation of a circle. Hence particle follows a circular path.