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Physics Case study (4 Marks)

Mechanical Properties of Fluids · Uttarakhand Board (UBSE) STD 11 Science (Uttarakhand - English Medium). 2 questions.

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Case study (4 Marks)

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2 questions · self-marked practice — reveal the answer and mark yourself.

Question 14 Marks
Read the passage given below and answer the following questions from 1 to 3. Bernoulli's Theorem It states that for the streamline flow of an ideal liquid through a tube, the total energy (the sum of pressure energy, the potential energy and kinetic energy) per unit volume remains constant at every cross-section throughout the tube.$\text{P}+\text{pgh}+\frac{1}{2}\text{pv}^2$ = constant
or $\frac{\text{P}}{\text{pg}}+\text{h}+\frac{1}{2}\frac{\text{v}^2}{\text{g}}$ = another constant Here, $\frac{\text{P}}{\text{pg}}$ = pressure head; h = potential head and $\frac{1}{2}\frac{\text{v}^2}{\text{g}}$ velocity head. If the liquid is flowing through a horizontal tube, then h is constant, then according to Bernoulli’s theorem,$\frac{\text{P}}{\text{pg}}+\frac{1}{2}\frac{\text{v}^2}{\text{g}}$ constant
Bernoulli’s theorem is based on law of conser - vation of energy.
  1. Bernoulli’s equation for steady, non-viscous, incompressible flow expresses the:
  1. Conservation of linear momentum
  2. Conservation of angular momentum
  3. Conservation of energy
  4. Conservation of mass
  1. Applications of Bernoulli’s theorem can be seen in:
  1. Dynamic lift of aeroplane
  2. Hydraulic press
  3. Helicopter
  4. None of these
  1. A tank filled with fresh water has a hole in its bottom and water is flowing out of it. If the size of the hole is increased, then:
  1. The volume of water flowing out per second will decrease.
  2. The velocity of outflow of water remains unchanged.
  3. The volume of water flowing out per second remains zero.
  4. Both (b) and (c)
Answer
  1. (c) Conservation of energy
Explanation:
Bernoullis equation for steady, non-viscous, in compressible flow express the conservation of energy.
  1. (a) Dynamic lift of aeroplane
Explanation:
The shape of the aeroplane wings is such that when it moves forward, the air molecules at the top of the wings have a greater velocity (relative to the wings) compared to the air molecules at the bottom.
Therefore in accordance with Bernoulli's principle, the pressure at the top of the wings is less than that at the bottom.
This results in a dynamic lift of the wings which balances the weight of the plane.
  1. (b) The velocity of outflow of water remains unchanged.
Explanation:
The velocity of outflow of water remains unchanged because it depends upon the height of water level and is independent of the size of the hole.
The volume depends directly on the size of the hole.
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Question 24 Marks
Read the passage given below and answer the following questions from $1$ to $5$. Surface Tension The property due to which the free surface of liquid tends to have minimum surface area and behaves like a stretched membrane is called surface tension. It is a force per unit length acting in the plane of interface between the liquid and the bounding surface i.e., $\text{S}=\frac{\text{F}}{\text{L}},$ where F = force acting on either side of imaginary line on surface and L = length of imaginary line. Surface tension decreases with rise in temperature. Highly soluble impurities increases surface tension and sparingly soluble impurities decreases surface tension.
  1. The excess pressure inside a soap bubble is three times than excess pressure inside a second soap bubble, then the ratio of their surface area is:
  1. 9 : 1
  2. 1 : 3
  3. 1 : 9
  4. 3 : 1
  1. Which of the following statements is not true about surface tension?
  1. A small liquid drop takes spherical shape due to surface tension.
  2. Surface tension is a vector quantity.
  3. Surface tension of liquid is a molecular phenomenon.
  4. Surface tension of liquid depends on length but not on the area.
  1. Which of the following statement is not true about angle of contact?
  1. The value of angle of contact for pure water and glass is zero.
  2. Angle of contact increases with increase in temperature of liquid.
  3. If the angle of contact of a liquid anda solid surface is less than 90°, then the liquid spreads on the surface of solid.
  4. Angle of contact depend upon the inclination of the solid surface to the liquid surface.
  1. Which of the following statements is correct?
  1. Viscosity is a vector quantity.
  2. Surface tension is a vector quantity.
  3. Reynolds number is a dimensionless quantity.
  4. Angle of contact is a vector quantity.
  1. A liquid does not wet the solid surface if the angle of contact is:
  1. 0°
  2. Equal to 90°
  3. Equal to 45°
  4. Greater than 90°
Answer
  1. (c) 1 : 9
Explanation:
Piecare, $\text{P}=\frac{4\text{S}}{\text{r}}$ or $\text{P}\propto\frac{1}{\text{r}}$
$\therefore\frac{\text{P}_1}{\text{p}_2}=\frac{\text{r}_2}{\text{r}_1}=\frac{3}{1}\ ...(\text{i})$ or $r_2 = 3r_1$
Also $\frac{\text{A}_1}{\text{A}_2}=\frac{4\pi\text{r}_1^2}{4\pi\text{r}_2^2}=\Big(\frac{\text{r}_1}{\text{r}_2}\Big)^2=\Big(\frac{\text{r}_1}{3\text{r}_1}\Big)^2=\frac{1}{9}$ (Using (i))
  1. (b) Surface tension is a vector quantity.
Explanation:
Surface tension is a scalar quantity because it has no specific direction for a given liquid.
  1. (b) Angle of contact depend upon the inclination of the solid surface to the liquid surface.
Explanation:
Angle of contact does not depend upon the inclination of the solid surface to the liquid surface.
  1. (c) Reynolds number is a dimensionless quantity.
Explanation:
Viscosity is a scalar quantity. Surface tension is a scalar quantity.
Reynolds number is a dimensionless quantity.
  1. (d) Greater than $90^\circ$
Explanation:
A liquid does not wet the solid surface if the angle of contact is obtuse (i.e. 8 > 90°).
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