Motion of a particle in x-y plane is described by a set of following equations x = 4 sin ( π/2 - ω t ) m and y = 4 sin (ω t) m. The path of the particle will be :

Solution

Physics sir · 3 steps

Rewrite x as a cosine, then square and add: the time drops out and a circle is left.

1. Rewrite x. Use sin(π/2 - θ) = cos θ. So x = 4 cos ω t and y = 4 sin ω t, two SHMs of equal amplitude at right angles, a quarter cycle apart.
2. Remove time. Square both and add. Since cos² ω t + sin² ω t = 1, the time dependence vanishes.

   x² + y² = 16(cos² ω t + sin² ω t) = 16

3. So. The path is x² + y² = 4², a circle of radius 4 m centred at the origin, option (a).

The idea to keep. Two perpendicular SHMs with a π/2 phase gap give an ellipse, and when the amplitudes are equal that ellipse becomes a circle. Always eliminate t to find the path.

Answer from the NTA final answer key. Solution by PrepWiser.