Question

A steel wire of diameter 0.8 mm and length 1 m is clamped firmly at two points A and B which are 1 m apart and in the same horizontal plane. A body is hung from the middle point of the wire such that the middle point sags 1 cm lower from the original position. Calculate the mass of the body. Given Young’s modulus of the material of wire = 2 × 10¹² dynes/cm².

Answer 1

Let the body be hung from the middle point C so that it sags through 1 cm to the point D as shown in the figure

∴ AD² = AC² + CD² = (50)² + (1)²

or AD = 50.01 cm

Increase in length = 0.01

Strain = 0.01/50 = 2 x 10^-4

Stress = 2 × 10¹² × 2 × 10^–4

= 4 × 10⁸ dynes/cm²

Tension T = Stress × Area of cross-section

= 4 × 10⁸ × π × (0.08)²

Since the mass m is in equilibrium,

mg = 2T cosθ or m = 2T cosθ/g