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A loop of mass M wid two identical rings of mass 3/2M each at its top hangs from a celling by an inextensible string. if the rings gently pushed horizontaly in opposite directions, find the angular distance covered by each ring when the tension in the string vanishes for once during their motion.

A loop of mass M wid two identical rings of mass 3/2M each at its top hangs from a celling by an inextensible string. if the rings gently pushed horizontaly in opposite directions, find the angular distance covered by each ring when the tension  in the string vanishes for once during their motion.

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1 Answers

Chetan Mandayam Nayakar
312 Points
10 years ago

let 'r' be radius of loop.It will be clear intuitively that the angle theta(answer) is acute. let w be angular speed of each ring.

(3M/4)w^2*r^2 =(3M/2)r(1-cos(theta)),2w^2*r=1-cos(theta),vertical component of centrifugal forces of 2 rings combined=

3Mw^2*rcos(theta)=Mg

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