Let's break down the problem step by step: **Given:** - Weight supported, \( W = 100 \) N - Height, \( h = 5 \) m - Velocity of water leaving the nozzle, \( v = 20 \) m/s - We need to find the diameter \( d \) of the nozzle. ### Step 1: Calculate the force exerted by the jet The force exerted by the jet to support the weight is equal to the weight itself, \( F = 100 \) N. ### Step 2: Jet force equation The force exerted by a jet of water striking a plate is given by: \[ F = \dot{m} v \] where \(\dot{m}\) is the mass flow rate. \[ \dot{m} = \rho Q \] where \(\rho\) is the density of water (\(\approx 1000 \) kg/m³), \(Q\) is the volumetric flow rate (\(Q = A v\)), and \(A\) is the area of the nozzle. So, \[ F = \rho Q v = \rho A v^2 \] \[ A = \frac{F}{\rho v^2} \] ### Step 3: Substitute values \[ A = \frac{100}{1000 \times (20)^2} = \frac{100}{1000 \times 400} = \frac{100}{400000} = 0.00025 \text{ m}^2 \] ### Step 4: Area to diameter \[ A = \frac{\pi d^2}{4} \] \[ d^2 = \frac{4A}{\pi} \] \[ d = \sqrt{\frac{4 \times 0.00025}{\pi}} \] \[ d = \sqrt{\frac{0.001}{3.1416}} \] \[ d = \sqrt{0.0003183} \] \[ d \approx 0.01785 \text{ m} = 17.85 \text{ mm} \] ### Step 5: Closest option Looking at the options: - 26.21 mm - 12.32 mm - 5.12 mm - **19.14 mm** **Closest answer is:** **19.14 mm** Let me know if you need the detailed calculations or further explanation!