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Two blocks each of mass M are connected ...

Two blocks each of mass M are connected to the ends of a light frame as shown in figure. The frame is rotated about the vertical line of symmetry. The rod breaks if the tension in it exceeds `T_0`. Find the maximum frequency with which the frame may be rotted without breaking the rod.

Text Solution

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Consider one of the blocks. If the frequencey of revolution is f, the angular velocity is `omega=2pif`. The acceleration towards the centre is `v^2/l=omega^2l=4pi^2f^2l`. The only horizontal force on the blck is the tension of the rod. At the point of breaking this foce is `T_0`. So from Newton's second law
`T_0=M.4pi^2f^2l`
or `f=1/(2pi) [T_0/(Ml)]^(1/2)`
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