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Two wires A and B are of the same material. Their lengths are in the ratio 1 : 2 and the diameter are in the ratio 2 : 1. If they are pulled by the same force, then increase in length will be in the ratio
We know that Young's modulus
Since Y, F are same for both the wires, we have,
So, ℓ_{1} : ℓ_{2} = 1 : 8
When an elastic material with Young’s modulus Y is subjected to stretching stress S, elastic energy stored per unit volume of the material is
Energy stored per unit volume
stress (stress / Young' s modulus)
(stress)^{2} /( Young ' s modulus)
The compressibility of water is 4 × 10^{–5} per unit atmospheric pressure. The decrease in volume of 100 cm^{3 }of water under a pressure of 100 atmosphere will be
Here, P = 100 atm,
K = 4 × 10^{–5} and V = 100 cm^{3}.
Hence, ΔV = 0.4 cm^{3}
The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied ?
So, extension,
[∵ F and Y are constant]
The ratio of is maximum for case (d).
Hence, option (d) is correct.
If the ratio of diameters, lengths and Young’s modulus of steel and copper wires shown in the figure are p, q and s respectively, then the corresponding ratio of increase in their lengths would be [NEET Kar. 2013]
From formula, Increase in length
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