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Two steel wires of the same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1:4, the ratio of their diameters is

Asked in JEE Main 9th Jan 2nd Shift 2020 · Energy stored in a stretched wire

• (1) √2:1
• (2) 1:√2
• (3) 2:1
• (4) 1:2

Step-by-step solution

Why the other options are wrong

• (2) comes from getting d⁴∝1/u right but then reading the given ratio the wrong way round, matching the wire with the smaller energy density to the smaller diameter; a thicker wire carries less stress, so it is the thicker wire that stores less per unit volume.
• (3) comes from using u∝1/(d²) instead of 1/(d⁴), that is, forgetting that the stress itself already carries one factor of the area and that u goes as the square of the stress.
• (4) comes from combines both slips above: the d² dependence and the inverted reading of 1:4.

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