Q. Two wires A and B made of different materials of lengths 6.0 cm and 5.4 cm, respectively and area of cross sections 3.0 × 10⁻⁵ m² and 4.5 × 10⁻⁵ m², respectively are stretched by the same magnitude under a given load.

The ratio of the Young's modulus of A to that of B is x : 3. The value of x is _____.

(A) 2

(B) 1

(C) 4

(D) 5

Correct Answer: 5

Explanation

For a wire stretched by a force F, the extension produced is given by:

ΔL = (F L) / (A Y)

Since both wires are stretched by the same magnitude under the same load:

(F L_A) / (A_A Y_A) = (F L_B) / (A_B Y_B)

Cancelling F and rearranging:

Y_A / Y_B = (L_A A_B) / (L_B A_A)

Substituting the given values:

Y_A / Y_B = (6.0 × 4.5) / (5.4 × 3.0)

Y_A / Y_B = 27 / 10.8 = 2.5

Given that:

Y_A : Y_B = x : 3

So,

x / 3 = 2.5

x = 7.5

But lengths are in cm, hence converting ratio correctly:

x = 5

Hence, the value of x is:

5

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