Two wires having the same length and material are stretched by the same force. Their diameters are in the ratio 1 : 3 . The ratio of strain energy per unit volume for these two wires (smaller to larger diameter), when stretched, is

Step-by-step solution

Strain energy per unit volume u = U V = 1 2 × s t r e s s × s t r a i n U V = 1 2 × F A × ∆ l l U V = 1 2 Stress × Stress Y ∴   u S u L = Y L Y S × ( Strain ( S ) Stress ( S ) ) 2 = ( A L A S ) 2 = ( r L 2 r S 2 ) 2 = ( 81 1 )