# NCERT Class 11 Physics Solutions: Chapter 10 – Mechanical Properties of Fluids-Part 12

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# Question 10.27

A plane is in level flight at constant speed and each of its two wings has an area of . If the speed of the air is over the lower wing and over the upper wing surface, determine the plane’s mass. (Take air density to be ).

The area of the wings of the plane,

Speed of air over the lower wing,

Speed of air over the upper wing,

Density of air,

Pressure of air over the lower wing

Pressure of air over the upper wing

The upward force on the plane can be obtained using Bernoulli’s equation as:

The upward force (F) on the plane can be calculated as:

Using Newton’s force equation, we can obtain the mass of the plane as:

Hence, the mass of the plane is about

Question 10.28:

In Millikan’s oil drop experiment, what is the terminal speed of an uncharged drop of radius and density ? Take the viscosity of air at the temperature of the experiment to be . How much is the viscous force on the drop at that speed? Neglect buoyancy of the drop due to air.

Terminal speed

Viscous force

Radius of the given uncharged drop,

Density of the uncharged drop,

Viscosity of air,

Density of air can be taken as zero in order to neglect buoyancy of air.

Acceleration due to gravity,

Terminal velocity is given by the relation:

Question 10.29:

Mercury has an angle of contact equal to with soda lime glass. A narrow tube of radius made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside? Surface tension of mercury at the temperature of the experiment is . Density of mercury

Angle of contact between mercury and soda lime glass,

Radius of the narrow tube,

Surface tension of mercury at the given temperature,

Density of mercury,

Dip in the height of mercury

Acceleration due to gravity,

Surface tension is related with the angle of contact and the dip in the height as:

Here, the negative sign shows the decreasing level of mercury. Hence, the mercury level dips by