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The particles move in the x-y plane according to the rules x=a\ sin\ \omega t  and   y=a\ cos \ \omega t. The particles are as follow:

Option: 1

An elliptical path

Option: 2

A circular path

Option: 3

A parabolic path


Option: 4

A straight-line path inclined equally to x and y-axis.

Answers (1)


Answer: (2) A circular path.


  x=a\ sin \omega t                                    

Or, \frac{x}{a}=\ sin\omega t    ---------------- (1)                   

And,    y=a\ cos\omega t       

Or,  \frac{y}{a}=a\ cos\omega t -------------- (2)      

Adding equation (1) and (2), we get:


Or,  x^2+y^2=a^2            

This is an equation of a circle, so the particle follows the circular path.

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