Question

A particle moves in x-y plane according to rule x = asin$\omega$t and y = acos$\omega$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

The correct option is B a circular path

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