A string is passing through a ring of mass m as shown. The ring rotates in a horizontal plane of radius r with a constant angular velocity. What should be the maximum speed of rotation so that the string does not get distorted?
A
rg
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B
√rg
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C
rg
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D
gr
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Solution
The correct option is B√rg FBD of ring of mass m:
Since there is only one string, tension is same throughout. Equating forces along horizontal direction : Tsin30∘+Tsin60∘=mv2r....(1) Equating forces along vertical direction : Tcos30∘+Tcos60∘=mg ....(2)
Dividing (1) by (2): Tsin30∘+Tsin60∘Tcos30∘+Tcos60∘=v2rg ⇒v2rg=1 ⇒v=√rg