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Question

Two wires of the same material (young's modules Y) and same length L but radii $$R$$ and $$2R$$ respectively are joined end to end and a weight $$W$$ is suspended from the combination as shown in the figure. the elastic potential energy in the system in equilibrium is 


A
3W2L4πR2Y
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B
3W2L8πR2Y
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C
5W2L8πR2Y
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D
W2LπR2Y
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Solution

The correct option is C $$\dfrac { 5{ W }^{ 2 }L }{ 8\pi { R }^{ 2 }Y }$$
$$W = {\dfrac{1}{2}}\times{F}\times{e} = {\dfrac{w^2L}{2AY}}$$

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

 = $${\dfrac{5w^2L}{8{\pi}R^2Y}}$$

Physics

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