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 1

Answer: (B)

$x=a\sin \omega t$ or $\frac{x}{a}=\sin \omega t$ ..(i)
$y=a\cos \omega t$ or $\frac{y}{a}=\cos \omega t$ ..(ii)
Squaring and adding, we get
$\frac{x^2}{a^2}+\frac{y^2}{a^2}=1$ $(\because {\cos }^2\omega t+{\sin }^2\omega t=1)$
or $x^2+y^2=a^2$
This is the equation of a circle. Hence particle follows a circular path.