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  • A particle moves such that its position vector <img alt="\widehat{r}\left ( t \right ) = cos\omega t\widehat{i} + sin \omega t\widehat{j}" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Cwidehat%7Br%7D%5Cleft%20%28%20t%20%5Cright%20%29%20%3D%20c

A particle moves such that its position vector \widehat{r}\left ( t \right ) = cos\omega t\widehat{i} + sin \omega t\widehat{j} where \omega is a constant and t is time. Then which of the following statements is true for the velocity \vec{v}(t) and acceleration \vec{a}(t) of the particle : 
Option: 1 \vec{v} and \vec{a} both are parallel to \vec{r}
Option: 2 \vec{v}is perpendicular to \vec{r}and \vec{a} is directed away from the origin
Option: 3 \vec{v} and \vec{a} both are perpendicular to \vec{r}
Option: 4 \vec{v} is perpendicular to \vec{r} and \vec{a} is directed towards the origin
 

Answers (1)

best_answer

\\\vec r=cos\omega t\ i+ sin\omega t\ j\\\vec v=\frac{d\vec r}{dt}=-\omega sin\omega t i+\omega cos\omega t j

\\\vec a=\frac{d\vec v}{dt}=-\omega ^2(cos\omega t\ i+ sin\omega t\ j)=-\omega^2 \vec r

implies a is anti parallel to r

\\\vec v. \vec r=0\\

Implies v is perpendicular to r

hence the correct option is (4). 

Posted by

vishal kumar

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