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A particle moves so that its position v...

A particle moves so that its position vertor is given by `overset rarr(r ) = cos omegat hatx + sin omegat haty`, where `omega` is a constant. Which of the following is true?

A

Velocity and acceleration both are perpendicular to `overset rarr r`

B

Velocity and acceleration both are parallel to `overset rarr r`

C

Velocity is perpendicular to `overset rarr r` and
acceleration is directed to wards the origin

D

Velocity is perpendicualr to `overset rarr r` and
acceleration is directed away from the origin

Text Solution

Verified by Experts

The correct Answer is:
C
`overset rarr r= cos omega t overset ^x+ sin omega t overset ^y`
`overset rarr V =- omega sin omega t overset ^ x + omega cos omega t overset ^ y`
`overset rarr a = - omega^(2) cos omega t overset^x + omega^(2)(- sin omega t) overset ^y `
`= - omega^(2) overset rarr r`
`overset rarr r. overset rarr V = 0`" " "hence" `overset rarr r bot overset rarrV`
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