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A bird with mass m perches at the middle...

A bird with mass m perches at the middle of a stretched string Show that the tension in the string is give by `T=(mg)/(2sin theta)`. Assume that each half of the string is straight.

Text Solution

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Initial position of wire = AOB. Final position of wire = ACB Let `theta` be the angle made by wire with horizontal, which is very small. Reasolving tension T of string in horizonts cancel while vertical components add and balance the weight.
For equilibrium `2T sintheta=W=mgimpliesT=(W)/(2sintheta)=mg//2sintheta`
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