### Question Recap **Question:** When a force \( F \) acts on a helical spring of wire diameter \( d \) and mean coil diameter \( D \), the maximum torsional shear stress \( \tau_{max} \) is given by: ### Options 1. \( \frac{8FD}{\pi d^3} \) 2. \( \frac{8FD}{\pi d^3} - \frac{4F}{\pi d^2} \) 3. \( \frac{16FD}{\pi d^3} - \frac{4F}{\pi d^2} \) 4. \( \frac{16FD}{\pi d^3} \) --- ## Solution For a helical spring: - Maximum torsional shear stress, \( \tau_{max} = \frac{8FD}{\pi d^3} \) This is a standard result in the mechanics of materials. #### **Correct Option:** **Option 1: \( \frac{8FD}{\pi d^3} \)** --- ### **Final Answer** \[ \boxed{\frac{8FD}{\pi d^3}} \] **(Option 1 is correct)**