The two-dimensional motion of a particle is described by $\vec{r}$ = A cos(ωt)( $\hat{i}+2\hat{j}$ ). Consider: (I) parabolic path, (II) elliptical path, (III) periodic motion, (IV) simple harmonic motion. Choose the correct combination.
Options

Question

The two-dimensional motion of a particle is described by $\vec{r}$ = A cos(ωt)( $\hat{i}+2\hat{j}$ ). Consider: (I) parabolic path, (II) elliptical path, (III) periodic motion, (IV) simple harmonic motion. Choose the correct combination.

Options

G1 Physics · Accepted Answer

Step 1: Both x and y coordinates are proportional to cos(ωt), with y=2x, so the particle moves along a fixed straight line, not a parabola or ellipse. Step 2: The coordinate varies sinusoidally with time, so the motion is periodic. Step 3: Motion along the fixed line is simple harmonic. Therefore statements III and IV only are correct. Final answer: D.

The two-dimensional motion of a particle is described by r ⃗ \vec{r} r = A cos(ωt)( i ^ + 2 j ^ \hat{i}+2\hat{j} i ^ + 2 j ^ ​ ). Consider: (I) parabolic path, (II) elliptical path, (III) periodic motion, (IV) simple harmonic motion. Choose the correct combination.

The two-dimensional motion of a particle is described by r ⃗ \vec{r} r = A cos(ωt)( i ^ + 2 j ^ \hat{i}+2\hat{j} i ^ + 2 j ^ ). Consider: (I) parabolic path, (II) elliptical path, (III) periodic motion, (IV) simple harmonic motion. Choose the correct combination.