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A particle moves so that its position vector is given by $\vec{r} = \cos ωt \vec{x} + \sin ωt \hat{y}$ , where $ω$ is a constant which of the following is true?

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Velocity is perpendicular to r→ and acceleration is directed away from the origin.

Velocity and acceleration both are perpendicular to r→

Velocity and acceleration both are parallel to r→

Velocity is perpendicular to r→ and acceleration is directed towards the origin.

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detailed solution

Correct option is D

r→ = cosωt x^+ sinωt y^v→ = −ωsinωt x^+ ωcosωt y^a→ = −ω2cosωt x^+ ωsinωt y^ = −ω2r→r→.v→ = 0 hence r→ ⊥ v→ a→ is directed towards the origin.

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A particle moves so that its position vector is given by r→ = cos ωt x→ +sin ωt y^, where ω is a constant which of the following is true?

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A particle moves so that its position vector is given by $\vec{r} = \cos ωt \vec{x} + \sin ωt \hat{y}$ , where $ω$ is a constant which of the following is true?