Question

The magnitude of displacement of a particle moving in a circle of radius a with constant angular speed w varies with time t as –

• A. 2a sin wt
• B. 2a sin$\frac{\omega t}{2}$
• C. 2a coswt
• D. 2a cos$\frac{\omega t}{2}$

Answer 1

Answer: (B)

2a sin$\frac{\omega t}{2}$

Answer 2

In time t particle has rotated an angle q = wt. Displacement

s = PQ =$\sqrt{QR^{2} + PR^{2}}$

=$\sqrt{(a\sin\omega t)^{2} + (a - a\cos\omega t)^{2}}$

s = 2a sin$\frac{\omega t}{2}$