Download the app

Questions  

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?

Unlock the full solution & 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
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→
NEW

Ready to Test Your Skills?

Check Your Performance Today with our Free Mock Tests used by Toppers!

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


Similar Questions

Find the dot product of A=i^+j^ and B=2i^-3j^+4k^ 

Get your all doubts cleared from
Sri Chaitanya experts

counselling
india
+91

phone iconwhats app icon