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)

a circular path

Answer 2

$x = a \sin \omega t$ 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.