A particle moves so that its position vector | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$\begin{array}{l} \,\,\,\,\,\,\,\,\,\,\,\,\,Give,\,\vec r = \cos \omega t\,\hat x + \sin \,\omega t\,\hat y\ 	herefore \,\,\,\,\vec v = \frac{{d\vec

Vedclass · Accepted Answer

Velocity is perpendicular to $\overrightarrow {\;r} \;$ and acceleration is directed towards the origin.

Vedclass · Answer

$\begin{array}{l} \,\,\,\,\,\,\,\,\,\,\,\,\,Give,\,\vec r = \cos \omega t\,\hat x + \sin \,\omega t\,\hat y\ 	herefore \,\,\,\,\vec v = \frac{{d\vec r}}{{dt}} =  - \omega \,\sin \,\omega t\,\hat x + \omega \,\cos \omega t\,\hat y\ \,\,\,\,\,\,\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyleightharpoonup$}}  \over a}  = \frac{{d\vec v}}{{dt}} =  - {\omega ^2}\,\cos \,\omega t\,\hat x - {\omega ^2}\,\sin \,\omega t\,\hat y =  - {\omega ^2}\vec r\ {m{Since}}\,position\,vector\,\left( {\bar r} ight)\,is\,directed\,away\ from\,the\,origin,\,so,\,acceleration\,\left( { - {\omega ^2}\bar r} ight)\ is\,directed\,towards\,the\,origin.\ Also,\ \vec r \cdot \vec v = \left( {\cos \omega t\,\hat x + \sin \,\omega t\,\hat y} ight) \cdot \left( { - \omega \sin \omega t\,\hat x + \omega \cos \omega t\,\hat y} ight)\  =  - \omega \sin \omega t\cos \omega t + \omega \sin \omega t\cos \omega t = 0\ \,\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \bar r\, \bot \bar v \end{array}$

A particle moves so that its position vector is given by $\overrightarrow {\;r} = cos\omega t\,\hat x + sin\omega t\,\hat y$ , where $\omega$ is a constant. Which of the following is true?

Similar Questions

In the given figure, $a = 15 \,m s^{- 2}$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R = 2.5\, m$ at a given instant of time. The speed of the particle is ........ $m/s$

A ball of mass $( m )=0.5 \ kg$ is attached to the end of a string having length $(L)$ $=0.5 m$. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is $324 \ N$. The maximum possible value of angular velocity of ball (in radian/s) is

A man is running with constant speed along a circular path of radius $2 \sqrt 2\, m$. He completes $1$ round in $10\, second$. Find instantaneous speed at $2.5 \,sec.$

If a particle is moving on a circular path with constant speed, then the angle between the direction of acceleration and its position vector w.r.t. centre of circle will be ............

A stone ties to the end of a string $1\,m$ long is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolution in $44$ seconds, what is the magnitude and direction of acceleration of the stone