Questions

# A particle moves so that its position vector is given by where $\omega$ is a constant.Which of the following is true?

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a
Velocity is perpendicular to r→ and acceleration is directed towards the origin.
b
Velocity is perpendicular to r→and acceleration is directed away from the origin
c
Velocity and acceleration both are perpendicular to r→
d
Velocity and acceleration both are parallel tor→
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detailed solution

Correct option is A

Given, r→=cosωt x^+sinωt y^∴v→=dr→dt=-ωsinωt x^+ωcosωt y^a→=dv→dt=-ω2cosωt x^-ω2sinωt y^=-ω2r→ Since position vector (r→) is directed away from the origin, so,  acceleration -ω2r→ is directed towards the origin. also,⇒r→⊥v→r→·v→=(cosωtx^+sinωty^)·(-ωsinωtx^+ωcosωty^)=-ωsinωtcosωt+ωsinωtcosωt=0

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