The two dimensional motion of a particle, described by is a/an A. parabolic path B. elliptical path C. periodic path D. simple harmonic motion Choose the correct answer from the options given below: [2024]

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Solution

Q.
The two dimensional motion of a particle, described by $\vec{r} = (\hat{i} + 2 \hat{j}) A \cos ω t$ is a/an

A. parabolic path
B. elliptical path
C. periodic path
D. simple harmonic motion

Choose the correct answer from the options given below: [2024]

1 B, C and D only

2 A, B and C only

3 A, C and D only

4 C and D only

Ans.
(4)

$\vec{r} = A \cos ω t \hat{i} + 2 A \cos ω t \hat{j}$

$x = A \cos ω t$ ...(i)

$y = 2 A \cos ω t$ ...(ii)

Dividing (i) by (ii), we get

$\frac{x}{y} = \frac{1}{2} [Equation of straight line]$

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