Question

A ring of radius r and mass per unit length m rotates with an angular velocity ωin free space. The tension in the ring is

• A. Zero
• B. $\frac{1}{2}m\omega^{2}r^{2}$
• C. mω²r²
• D. mrω²

Answer 1

Answer: (C)

mω²r²

Answer 2

Let T = tension in the ring. For the section AB, the net force is 2T sin θ. As θ is small, therefore 2T sin θ ~ 2Tθ, and the net force is towards C. Mass of section AB = (2rθ) m. For circular motion,

(2rθm)rω² or T = mr²ω².