A ring of radius r and mass per unit length m rotates with an angular velocity ω ω in free space. The tension in the ring is
A
Zero
B
C
m ω ω 2 r 2
D
mr ω ω 2
Text Solution
Verified by ExpertsThe correct answer is:
C
Let T = tension in the ring. For the section AB, the net force is 2T sin θ θ . As θ θ is small, therefore
2T sin θ θ ~ 2T θ θ , and the net force is towards C. Mass of section AB = (2r θ θ ) m. For circular motion,
(2r θ θ m)r ω ω 2 or T = mr 2 ω ω 2 .
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