SATHEE: Motion in a Plane - Result Question 41

Motion in a Plane - Result Question 41

44. A particle moves so that its position vector is given by $\vec{r} = \cos ω t \hat{x} + \sin ω t \hat{y}$ . Where $ω$ is a constant. Which of the following is true?[2016]

(a) Velocity and acceleration both are perpendicular to $\vec{r}$

(b) Velocity and acceleration both are parallel to $\vec{r}$

(d) Velocity is perpendicular to $\vec{r}$ and acceleration is directed away from the origin

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Answer:

Correct Answer: 44. (c)

Solution:

$\vec{r} = \cos ω t \hat{x} + \sin ω t \hat{y}$

$∴$ Velocity vector, $\vec{v} = - ω \sin ω t \hat{x} + ω \cos ω t$ $\hat{y}$ acceleration vector,

$\vec{a} = - ω^{2} \cos ω t \hat{x} - ω^{2} \sin ω t \hat{y} = - ω^{2} \vec{r}$

$\vec{r} \cdot \vec{v} = 0$ hence $\vec{r} ⊥ \vec{v}$ and $\vec{a}$ is directed towards the origin.

Nothing actually moves in the direction of the angular velocity vector $\vec{ω}$ . The direction of $\vec{ω}$ simply represents that the circular motion is taking place in a plane perpendicular to it.

Motion in a Plane - Result Question 41

44. A particle moves so that its position vector is given by $\vec{r} = \cos ω t \hat{x} + \sin ω t \hat{y}$ . Where $ω$ is a constant. Which of the following is true?[2016]

Answer:

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Motion in a Plane - Result Question 41

44. A particle moves so that its position vector is given by r→=cos⁡ωtx^+sin⁡ωty^. Where ω is a constant. Which of the following is true?[2016]

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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44. A particle moves so that its position vector is given by $\vec{r} = \cos ω t \hat{x} + \sin ω t \hat{y}$ . Where $ω$ is a constant. Which of the following is true?[2016]