Important questions based on NCERT syllabus for Chapter 10 - Mechanical Properties of Fluids:
Question-1: Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli’s equation? Explain.
Solution: No, it does not matter if one uses gauge instead of absolute pressures in applying Bernoulli’s equation, provided the atmospheric pressure at the two points where Bernoulli’s equation is applied are significantly different.
Question-2: There are two vessels of different shapes but equal base areas. The second vessel takes half the volume of water the first takes in getting filled up to a common height. Will the force on the base of the two vessels exerted by water be the same? If it is so, why do these vessels filled with water up to the same height have different weights?
As the base area is the same the pressure and thus the force acting on the two vessels will also be the same. However, force is also exerted on the walls of the vessel, which have a nonvertical component when the walls are not perpendicular to the base. The net non-vertical component on the sides of the vessel is lesser for the second vessel than the first. Therefore, the vessels have different weights despite having the same force on the base.
Question-3: A U-shaped wire is dipped in a soap solution, and removed. A thin soap film formed between the wire and a light slider supports a weight of 1.5 x 10^-2 N (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film?
Solution: In present case force of surface tension is balancing the weight of 1.5 x 10^-2 N, hence force of surface tension, F = 1.5 x 10^-2 N.
Total length of liquid film, l = 2 x 30 cm = 60 cm = 0.6 m because the liquid film has two surfaces.
Surface tension, T = F/l =1.5 x 10^-2 N/0.6m =2.5 x 10^-2 Nm^-1