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
Another one Kourtney😝💕 — let's solve it. 10. The figure below shows a water U-tube manometer used to measure the gas pressure of a gas cylinder. Step 1: Convert the density of the liquid to SI units. = 0.8 g/cm^3 = 0.8 × 1 kg1000 g × (100 cm1 m)^3 = 0.8 × 1000 kg/m^3 = 800 kg/m^3 Step 2: Determine the height difference of the liquid columns and convert to meters. The liquid level at X is 9 cm below the tap. The liquid level at Y is 9 cm above the level Z (which is at the same horizontal level as X). The total height difference h is the sum of these two displacements. h = 9 cm + 9 cm = 18 cm h = 0.18 m Step 3: Calculate the pressure due to the liquid column difference. Assume the acceleration due to gravity g = 10 m/s^2. P_liquid = g h P_liquid = 800 kg/m^3 × 10 m/s^2 × 0.18 m P_liquid = 1440 Pa Step 4: Calculate the gas pressure in N/m^2 (Pascals). Since the liquid level in the arm connected to the gas supply (X) is lower than the level in the arm open to the atmosphere (Y), the gas pressure is greater than the atmospheric pressure. P_gas = P_atm + P_liquid P_gas = 101400 Pa + 1440 Pa P_gas = 102840 Pa Step 5: Convert the gas pressure to cmHg. To convert pressure to the height of a mercury column, use the formula P = _Hg g h_Hg. The density of mercury (_Hg) is 13600 kg/m^3. h_Hg = P_gas_Hg g h_Hg = 1