Question

A 4 kg stone is attached to a steel wire being whirled at a constant speed of \( 12 \) m/s in a horizontal circle. The wire is 4 m long with a diameter of 2 mm, and Young’s modulus is \( 2 \times 10^{11} \) Nm\(^2\). The strain in the wire is:

• A. \( 2.3 \times 10^{-4} \)
• B. \( 2.3 \times 10^{-5} \)
• C. \( 4.6 \times 10^{-4} \)
• D. \( 6.9 \times 10^{-4} \)

Hint:

For problems involving strain, use Young’s modulus and the stress formula.

Answer 1

The Correct Option is A

Step 1: Calculating the Tension in the Wire Centripetal force provides tension: \[ T = \frac{m v^2}{r} = \frac{4 \times 12^2}{4} = 144 N \] Step 2: Calculating Strain Strain is given by: \[ \text{Strain} = \frac{\text{Stress}}{\text{Young’s Modulus}} \] Stress: \[ \text{Stress} = \frac{T}{A} = \frac{144}{\pi (1 \times 10^{-3})^2} = \frac{144}{\pi \times 10^{-6}} \] \[ = 4.6 \times 10^7 \] \[ \text{Strain} = \frac{4.6 \times 10^7}{2 \times 10^{11}} \] \[ = 2.3 \times 10^{-4} \] Thus, the correct answer is option (1).