Question

A particle moves in $x y$ -plane according to the 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 $y$ -axis

Answer 1

Answer: (B)

Given, $\frac{x}{a}=\sin \omega t$ and $\frac{y}{a}=\cos \omega t$
Now $\frac{y^{2}}{a^{2}}+\frac{x^{2}}{a^{2}}=1$
$\Rightarrow y^{2}+x^{2}=a^{2}$
This is equation of a circle having radius a.