Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

A particle moves in the x-y plane according to rule $x = a \sin \omega t$ and $y = a \cos \omega t$ . The particle follows:

an elliptical path.

a circular path.

a parabolic path.

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

Identify the Parametric Equations: The motion of the particle is described by the coordinates: $x = a \sin \omega t$ $y = a \cos \omega t$
Eliminate the Time Parameter ( $t$ ): To determine the path (trajectory), we eliminate $t$ by squaring both equations and adding them together. $x^2 = a^2 \sin^2 \omega t$ $y^2 = a^2 \cos^2 \omega t$ $x^2 + y^2 = a^2 (\sin^2 \omega t + \cos^2 \omega t)$
Apply Trigonometric Identity: Using $\sin^2 \theta + \cos^2 \theta = 1$ : $x^2 + y^2 = a^2$
Conclusion: The resulting equation represents a circle with its center at the origin $(0, 0)$ and a constant radius $a$ . Thus, the particle performs uniform circular motion .

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