Q.

A particle moves so that its position vector is given by r→=cosωt x^+sinωt y^, where ω is a constant.Which of the following is true?

Moderate

Unlock the Full Solution and Master the Concept

Get a detailed solution and exclusive access to our masterclass to ensure you never miss a concept

By Expert Faculty of Sri Chaitanya

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

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 tor→

answer is 1.

(Detailed Solution Below)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

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

Choose your Grade and Exam

Connect with our

Expert Counsellors

access to India's best teachers with a record of producing top rankers year on year.

+91

We will send a verification code via OTP.