Final answer:
To find the gauge pressure difference between the balloon and the jar in the manometer, we can calculate the pressure difference in each arm and subtract them. The pressure difference in the balloon arm can be calculated using ρgh, where ρ is the density of water and h is the height of the water column.
Step-by-step explanation:
The manometer in the figure consists of two arms connected by a U-shaped tube. One arm is connected to the balloon and contains water while the other arm is connected to the jar and contains mercury. The height of the fluid in both arms is given as h = 0.0500 m. To find the gauge pressure difference (pA - pB), we need to calculate the pressure difference in each arm and subtract the values.
Using the density of water (ρ = 1000 kg/m^3) and the height of the water column (h), we can calculate the pressure difference in the balloon arm using the equation pA = ρgh. Substituting the values, we get pA = 1000 kg/m^3 * 9.8 m/s^2 * 0.0500 m = 490 Pa.
Similarly, using the density of mercury (ρ = 13,600 kg/m^3) and the height of the mercury column (h), we can calculate the pressure difference in the jar arm using the equation pB = ρgh. Substituting the values, we get pB = 13,600 kg/m^3 * 9.8 m/s^2 * 0.0500 m = 6,686 Pa.
Finally, to find the gauge pressure difference (pA - pB), we subtract the pressure in the jar arm from the pressure in the balloon arm, resulting in (pA - pB) = 490 Pa - 6,686 Pa = -6,196 Pa. Therefore, the gauge pressure difference between the balloon and the jar is -6,196 Pa.