Q. The position vector of a particle $\vec{R}$ as a function of time is given by : $\vec{R} = 4\sin(2\pi t)\hat{i} + 4\cos(2\pi t)\hat{j}$ Where R is in meters, t is in seconds and $\hat{i}$ and $\hat{j}$ denote unit vectors along x and y-directions, respectively. Which one of the following statements is wrong for the motion of particle ?
A) Path of the particle is a circle of radius 4 meter
B) Acceleration vectors is along $-\vec{R}$
C) Magnitude of acceleration vector is $\frac{v^2}{R}$ where v is the velocity of particle.
D) Magnitude of the velocity of particle is 8 meter/second
Explanation
[Solution] Uniform circular motion of radius 4 m with ω = 2π: |v| = ωR = 8π m/s, not 8 m/s. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.