Question

Position vector of a particle moving in x-y plane at time t is $\overset{\rightarrow}{r}$= a (1 – coswt) $\widehat{i}$+ a sin wt $\widehat{j}$. The path of the particle is :

• A. Circle of radius a and centre at (a, 0)
• B. A circle of radius a and centre at (0, 0)
• C. An ellipse
• D. Neither a circle nor an ellipse

Answer 1

Answer: (A)

Circle of radius a and centre at (a, 0)

Answer 2

Particle is moving in a circle of radius a and centre (a, 0) with constant angular velocity w. At time t = 0 particle is at origin and it starts rotating clockwise. At time t it has rotated an angle q given by :

q = wt

y = a sin q = a sin wt

and x = a – a cos q = a (1 – cos wt)

\ $\overset{\rightarrow}{r}$= a (1 – cos wt) $\widehat{i}$+ a sin wt $\widehat{j}$