Question

Stone of 0.5 kg mass is attached to one end of a 0.8m long aluminium wire 0.7 mm in diameter and suspended vertically. The stone is now rotated in a horizontal plane at a rate such that the wire makes an angle of 85° with the vertical. Find the increase in length of the wire (in mm). (The Young's modulus of aluminium = 7 × 10¹⁰N/m²) (sin 85° = 0.9962, cos 85° = 0.0872 g = 10m/s²).

• A. 1.70 mm
• B. 0.85 mm
• C. 3.40 mm
• D. 0.425 mm

Answer 1

Answer: (A)

1.70 mm

Answer 2

The tension in the wire is determined by the weight of the stone and the angle it makes with the vertical ($T = \frac{mg}{\cos \theta}$). This tension causes an elastic extension in the wire, calculated using Young's modulus ($\Delta L = \frac{T L_0}{A Y}$). Substituting the given values and calculating yields the increase in length.