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QUESTION: 1

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

Solution:

We know that Young's modulus

Since Y, F are same for both the wires, we have,

So, ℓ_{1} : ℓ_{2} = 1 : 8

QUESTION: 2

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

Solution:

Energy stored per unit volume

stress (stress / Young' s modulus)

(stress)^{2} /( Young ' s modulus)

QUESTION: 3

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

Solution:

Here, P = 100 atm,

K = 4 × 10^{–5} and V = 100 cm^{3}.

Hence, ΔV = 0.4 cm^{3}

QUESTION: 4

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied ?

Solution:

So, extension,

[∵ F and Y are constant]

The ratio of is maximum for case (d).

Hence, option (d) is correct.

QUESTION: 5

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]

Solution:

From formula, Increase in length

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