# NCERT Class 11 Physics Solutions: Chapter 10 – Mechanical Properties of Fluids-Part 13

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**Question 10.30:**

Two narrow bores of diameters are joined together to form a U-tube open at both ends. If the U-tube contains water, what is the difference in its levels in the two limbs of the tube? Surface tension of water at the temperature of the experiment is . Take the angle of contact to be zero and density of water to be

**Answer:**

Diameter of the first bore,

Hence, the radius of the first bore,

Diameter of the second bore,

Hence, the radius of the second bore,

Surface tension of water,

Angle of contact between the bore surface and water,

Density of water,

Acceleration due to gravity,

Let be the heights to which water rises in the first and second tubes respectively. These heights are given by the relations:

The difference between the levels of water in the two limbs of the tube can be calculated as:

Hence, the difference between levels of water in the two bores is

**Question 10.31:**

(a) It is known that density of air decreases with height as

Where is the density at sea level, and is a constant. This density variation is called the law of atmospheres. Obtain this law assuming that the temperature of atmosphere remains a constant (isothermal conditions). Also assume that the value of gremials constant.

(b) A large He balloon of volume is used to lift a payload of Assume that the balloon maintains constant radius as it rises. How high does it rise? [Take ].

**Answer:**

**For**

Volume of the balloon,

Mass of the payload,

Acceleration due to gravity,

Density of the balloon

Height to which the balloon rises

Density of air decreases with height as:

This density variation is called the law of atmospherics.

It can be inferred from equation that the rate of decrease of density with height is directly proportional to , i.e.,

Where, is the constant of proportionality.

Height changes from while density changes from

Integrating the sides between these limits, we get:

Comparing equation we get:

From equation

For

Density

From Equation we can obtainas:

Hence, the balloon will rise to a height of