NEET Physics Two Dimensional Motion NEET PYQ-Two Dimensional Relative Motion

A particle moves in \[x-y\] plane according to rule \[x=a\sin \omega t\] and \[y=a\cos \omega t\]. The particle follows [AIPMT (M) 2010]

A) an elliptical path

B) a circular path

C) a parabolic path

D) a straight line path inclined equally to \[x\] and \[y-\]axes

Correct Answer: B

Solution :

\[x=a\sin \omega t\Rightarrow \frac{x}{a}=\sin \omega t\]

\[x=a\cos \omega t\Rightarrow \frac{x}{{{a}^{2}}}=\cos \omega t\]

\[\therefore \] \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] or \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]

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