Question

A particle moves in $xy$ -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.