Let's analyze the question in the image: **Question:** Calculate the angular acceleration of the rod shown in the figure. Consider hinge at C and the mass of the rod is 4 kg. Given: - Length of rod (\( L \)) = 450 mm = 0.45 m - Distance from hinge to center of mass (\( r \)) = 225 mm = 0.225 m (since it's the midpoint) - Force (\( P \)) = 75 N - Mass (\( m \)) = 4 kg ### Step 1: Find the Moment of Inertia For a rod rotating about one end: \[ I_C = \frac{1}{3} m L^2 = \frac{1}{3} \times 4 \times (0.45)^2 = \frac{1}{3} \times 4 \times 0.2025 = \frac{1}{3} \times 0.81 = 0.27 \text{ kg·m}^2 \] ### Step 2: Calculate the Torque The force \( P \) acts perpendicular to the rod at the end, so torque (\( \tau \)) about C is: \[ \tau = P \times L = 75 \times 0.45 = 33.75 \text{ N·m} \] ### Step 3: Calculate Angular Acceleration Using Newton's second law for rotation: \[ \tau = I_C \alpha \] \[ \alpha = \frac{\tau}{I_C} = \frac{33.75}{0.27} \approx 125 \text{ rad/s}^2 \] ### Step 4: Match to Choices Let's compare with the given choices: - α = 90 rad/s² - α = 125 rad/s² - α = 81 rad/s² - α = 107 rad/s² **Correct answer:** \[ \boxed{\alpha = 125 \text{ rad/s}^2} \]