Q136 / 200 · NEET 2024 (Re-NEET) · Physics

The two-dimensional motion of a particle, described by $\vec{r}=(\hat{i}+2 \hat{j}) A \cos \omega t$ is a/an: A. parabolic path B. elliptical path C. periodic motion D. simple harmonic motion Choose the correct answer from the options given below:

  • A
    B, C and D only
  • B
    A, B and C only
  • C
    A, C and D only
  • Correct answer
    D
    C and D only

Solution

$\vec{r}=(\hat{i}+2 \hat{j}) A \cos \omega t$ $x=A \cos \omega t$ $y=2 A \cos \omega t$ $y=2 x$ The path is straight line. The motion is SHM and periodic as $\frac{d r}{d t}=-(\hat{i}+2 \hat{j}) \omega A \sin \omega t$ $\frac{d^2 r}{d t^2}=-(\hat{i}+2 \hat{j}) \omega^2 A \cos \omega t$ $\vec{a}=-\omega^2 \vec{r}$

Hence, the correct answer is option: 'D'.

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