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  4. Two wires of the same material and same length but diameters in the ratio 1: 2 are stretched by the same force. The potential energy per unit volume of the two wires will be in the ratio

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Q. Two wires of the same material and same length but diameters in the ratio 1 : 2 are stretched by the same force. The potential energy per unit volume of the two wires will be in the ratio

KEAMKEAM 2011Motion in a Plane

Solution:

$ U = \frac{ 1}{ Z } \frac{ \sigma^2 }{ Y } $
$ \Rightarrow U \propto \sigma^2 \propto \frac{ 1}{ A^2 } $
$ \frac{ U_1 }{ U_2 } = \frac{ A_2^2 }{ A_1^2 } $
= $ \frac{ d_2^2 }{ d_1^2 } = \frac{16}{ 1} $