NCERT Class 11 Physics Solutions: Chapter 10 – Mechanical Properties of Fluids-Part 10

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Question 10.22:

A manometer reads the pressure of a gas in an enclosure as shown in Figure. (a) When a pump removes some of the gas, the manometer reads as in Figure(b) The liquid used in the manometers is mercury and the atmospheric pressure is of mercury.

Give the absolute and gauge pressure of the gas in the enclosure for cases (a) and (b), in units of cm of mercury.

How would the levels change in case (b) if of water (immiscible with mercury) are poured into the right limb of the manometer? (Ignore the small change in the volume of the gas).

A manometer reads the pressure of a gas in an enclosure as s …

Figure Shown the Manometer Reads the Pressure of a Gas

Answer:

The absolute and gauge pressure of the gas in the enclosure for cases :

(a) and

(b) in units of cm of mercury:

Explanation:

For figure

Atmospheric pressure,

Difference between the levels of mercury in the two limbs gives gauge pressure

Hence, gauge pressure is of .

Absolute pressure Atmospheric pressure Gauge pressure

For figure

Difference between the levels of mercury in the two limbs

Hence, gauge pressure is of

Absolute pressure Atmospheric pressure Gauge pressure

The levels change in case if of water (immiscible with mercury) are poured into the right limb of the manometer: 19 cm

Explanation:

of water is poured into the right limb of figure

Relative density of mercury

Hence, a column of of water is equivalent to of mercury.

Let be the difference between the levels of mercury in the two limbs.

The pressure in the right limb is given as:

Atmospheric pressure

The mercury column will rise in the left limb.

Hence, pressure in the left limb,

Equating equations we get:

Hence, the difference between the levels of mercury in the two limbs will be

Question 10.23:

Two vessels have the same base area but different shapes. The first vessel takes twice the volume of water that the second vessel requires to fill up to a particular common height. Is the force exerted by the water on the base of the vessel the same in the two cases? If so, why do the vessels filled with water to that same height give different readings on a weighing scale?Answer: Yes

Explanation:

Two vessels having the same base area have identical force and equal pressure acting on their common base area. Since the shapes of the two vessels are different, the force exerted on the sides of the vessels has non-zero vertical components. When these vertical components are added, the total force on one vessel comes out to be greater than that on the other vessel. Hence, when these vessels are filled with water to the same height, they give different readings on a weighing scale.