### 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

## Show Answer

#### 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.