NEET Solved Paper 2016 Question 27
Question: A particle moves so that its position vector is given by $ \overrightarrow{{}r}=\cos ,\omega t,\widehat{x}+\sin ,\omega ,t,\widehat{y}. $ Where $ \omega $ is a constant. Which of the following is true?
Options:
A) Velocity and acceleration both are perpendicular to r $ \vec{r}. $
B) Velocity and acceleration both are parallel to $ \vec{r}. $
C) Velocity is perpendicular to $ \vec{r}. $ and acceleration is directed towards the origin
D) Velocity is perpendicular to $ \vec{r}. $ and acceleration is directed away from the origin
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Answer:
Correct Answer: C
Solution:
- $ \vec{r}=\cos \omega t,\hat{x},+sin\omega t,\hat{y} $ $ \vec{v}=-\omega \sin \omega t,\hat{x}+\omega \cos \omega t,\hat{y} $ $ \vec{a}=-{{\omega }^{2}}\cos \omega t,\hat{x}+\omega \sin \omega t,\hat{y}=-{{\omega }^{2}}\vec{r} $ $ \vec{r}.\vec{v}=0 $ hence $ \vec{r}\bot \vec{v} $ $ \vec{\alpha } $ is directed towards the origin.
