Question

The displacement of a particle is given by r=A(i.cos⍵t+j.sin⍵t). The motion of the particle is
(a) simple harmonic
(b) on a straight line
(c) on a circle
(d) with constant acceleration.

Answer 1

Answer ⇒ Option (c.) On a circle.

Explanation ⇒ Since, the give equation is in the vector form.

Let us convert it into Scalar form.

Therefore Magnitude of r = √[A²(Cos²wt + Sin²wt)]

∴ |r| = A

This Means, Position vector is always constant in magnitude and not in direction. This can't be the case of the S.H.M. beaus there Distance used to vary.

Also, It can't be in straight lines, because there also happens the same.

But in Circle, the distance from center upto radius is constant, but only direction changes.

Hence, this is the answer.

Hope it help.