Question

A wire extends by 0.02 cm when loaded with 2 gm. If its length is 2 m and radius is 0.05
cm. Calculate Young’s modulus.​

Answer 1

Explanation:

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Answer 2

The value of Young's Modulus will be 2.54 * 10⁸ N/m²

Given,

Extension = x = 0.02 cm = 2 * 10⁻⁴ m

Mass = m = 2 gm = 2 * 10⁻³ kg

Length = L = 2 m

Radius of wire =  r = 0.05 cm = 5 * 10⁻⁴ m

To Find,

Young's Modulus (Y)

Solution,

Young's Modulus determines the amount of tension that a material can withstand when under extension or compression.

Using the formula,

Y = $\frac{F*L}{A*x}$

F = mg = 2 * 10⁻³ * 10 = 2 * 10⁻² N

A = Area of cross section of wire

A = πr² = 3.14 *  5 * 10⁻⁴ *  5 * 10⁻⁴

A = 78.5 * 10⁻⁸ m²

Y = $\frac{2*2}{2*78.5}$ * 10¹⁰ = 2.54 * 10⁸ N/m²

Thus, the value of Young's Modulus comes out to be 2.54 * 10⁸ N/m²

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