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
Step 1: Identify the given values and the formula for hydrostatic pressure. The problem provides the following information: • Density of the liquid, = 2000 kgm^-3 (assuming "kgm-1" is a typo and should be kgm^-3 for density). • Pressure, P = 9100 Nm^-2 (assuming "9100nm" is a typo and should be Nm^-2 or Pascals for pressure). • Acceleration due to gravity, g = 10 ms^-2. The formula for hydrostatic pressure is: P = g h where P is the pressure, is the density of the liquid, g is the acceleration due to gravity, and h is the depth. Step 2: Rearrange the formula to solve for depth (h). To find the depth, we rearrange the formula: h = (P)/( g) Step 3: Substitute the values and calculate the depth. Substitute the given values into the rearranged formula: h = 9100 Nm^-2(2000 kgm^-3)(10 ms^-2) h = 9100 Nm^-220000 kgm^-2s^-2 Since 1 N = 1 kg · m · s^-2, then 1 Nm^-2 = 1 kg · m · s^-2 · m^-2 = 1 kg · m^-1 · s^-2. So the units cancel out to meters: h = (9100)/(20000) m h = 0.455 m The depth at which the pressure in the liquid will be 9100 Nm^-2 is 0.455 m.