This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Hey — ready when you are. a) Explain why height h is less than 20 cm. Liquid X is denser than liquid Y (_X = 1000 kg/m^3 and _Y = 800 kg/m^3). For the pressures to be equal at the same horizontal level in the U-tube, the column of the denser liquid (X) must be shorter than the column of the less dense liquid (Y). Therefore, height h must be less than 20 cm. b) Determine the height h. Step 1: Identify the given values. Density of liquid X, _X = 1000 kg/m^3 Density of liquid Y, _Y = 800 kg/m^3 Height of liquid Y, H_Y = 20 cm = 0.20 m Height of liquid X, H_X = h Step 2: Apply the principle of equal pressure at the same horizontal level. The pressure exerted by a liquid column is given by P = g H. At the interface level, the pressure from both columns must be equal. P_X = P_Y _X g H_X = _Y g H_Y Step 3: Solve for h. Cancel g from both sides: _X H_X = _Y H_Y Substitute the known values: 1000 kg/m^3 × h = 800 kg/m^3 × 0.20 m 1000 h = 160 h = (160)/(1000) m h = 0.16 m Convert the height to centimeters: h = 0.16 × 100 cm h = 16 cm The height h is 16 cm. Send me the next one 📸