Let's break down the question and solve it step by step. ### **Given Data:** - **Length of bar (L):** 1.5 m = 1500 mm - **Energy absorbed (U):** 50 Nm = 50,000 Nmm - **Stress (σ):** 200 MPa = 200 N/mm² - **Elastic modulus (E):** 95 GPa = 95,000 N/mm² ### **Formula for energy absorbed by a bar under tension:** \[ U = \frac{\sigma^2}{2E} \cdot V \] Where: - \( U \) = Energy absorbed - \( \sigma \) = Stress - \( E \) = Elastic modulus - \( V \) = Volume of the bar For a round bar: \[ V = A \cdot L = \frac{\pi}{4} d^2 L \] So, \[ U = \frac{\sigma^2}{2E} \cdot \frac{\pi}{4} d^2 L \] Now, solve for diameter \( d \): \[ U = \frac{\sigma^2}{2E} \cdot \frac{\pi}{4} d^2 L \] \[ U = \frac{\pi \sigma^2 d^2 L}{8E} \] \[ d^2 = \frac{8EU}{\pi \sigma^2 L} \] \[ d = \sqrt{\frac{8EU}{\pi \sigma^2 L}} \] ### **Substitute the values:** - \( E = 95,000 \) N/mm² - \( U = 50,000 \) Nmm - \( \sigma = 200 \) N/mm² - \( L = 1500 \) mm \[ d = \sqrt{\frac{8 \times 95,000 \times 50,000}{\pi \times (200)^2 \times 1500}} \] Calculate the numerator: \[ 8 \times 95,000 \times 50,000 = 38,000,000,000 \] Calculate the denominator: \[ \pi \times (200)^2 \times 1500 = 3.1416 \times 40,000 \times 1500 = 188,496,000 \] \[ d = \sqrt{\frac{38,000,000,000}{188,496,000}} \] \[ d = \sqrt{201.6} \] \[ d \approx 14.2 \text{ mm} \] ### **Answer:** The correct answer is: **14.20 mm**.