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Question

Two light wires made up of the same material (Young Modulus, Y) have length $$L$$ each and radii $$R$$ and $$2R$$ respectively, They are joined together and suspended from a rigid support. Now a weight $$W$$ attached to the free end of the joint wire as shown in the figure. Find the elastic potential energy stored in the system due to the extension of the wire.
1269610_9d4b87731cdb4d03a5f97e36a905d64e.png


Solution

W = $$ \dfrac{1}{2} F \times e = \dfrac{F^2 l }{2AY}$$

W = $$ \dfrac{W^2 L }{2 ( \pi R^2 ) Y}    + \dfrac{W^2 L}{2 \pi ( 2 R )^2 Y}$$

  = $$ \dfrac {5 W^2 L}{8 \pi R^2 Y}$$

Physics

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