Question

The motion of a particle is given by \(X = a \cos t\), \(Y = a \sin t\) and \(Z = t\). The trajectory traced by the particle as a function of time is:

• A. Helix
• B. Circular
• C. Elliptical
• D. Straight line

Hint:

Helical trajectories are common in physics, representing combined rotational and translational motion, such as in a spring or screw.

Answer 1

The Correct Option is A

Step 1: Analyze the motion in the \( XY \) plane.
The parametric equations \( X = a \cos t \) and \( Y = a \sin t \) describe a circle in the \( XY \) plane.

Step 2: Consider the motion along \( Z \).
The \( Z \) coordinate increases linearly with time \( t \), indicating a vertical motion component.

Step 3: Combine the motions.
Combining the circular motion in the \( XY \) plane with the linear increase in \( Z \) gives a helical trajectory.