Vidaara.orgClass 11 · Physics
CodeVID-P11-09-BVB-01
Buoyancy, Viscosity & Bernoulli's Principle — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
A body floats when its average density is:
- A.greater than the fluid's
- B.less than the fluid's
- C.equal to zero
- D.infinite
2.
The SI unit of the coefficient of viscosity is:
- A.$\text{Pa}$
- B.$\text{Pa}\cdot\text{s}$
- C.$\text{N/m}$
- D.$\text{m}^2/\text{s}$
3.
Stokes' law for the viscous drag on a sphere is:
- A.$F=6\pi\eta r v$
- B.$F=\frac{6\pi r v}{\eta}$
- C.$F=6\pi\eta r^2 v$
- D.$F=\pi\eta r v$
4.
The equation of continuity states that $Av$ is:
- A.increasing
- B.decreasing
- C.constant
- D.zero
5.
Aeroplane lift is explained by:
- A.Pascal's law
- B.Archimedes' principle
- C.Bernoulli's principle
- D.Stokes' law
Section B — Short Answer (2 marks)
3 × 2 = 6 marks
6.
State Archimedes' principle.
7.
Define terminal velocity.
8.
Water flows from a $6\ \text{cm}^2$ pipe at $4\ \text{m/s}$ into a $2\ \text{cm}^2$ pipe. Find the new speed.
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
9.
Derive the expression for the terminal velocity of a sphere falling through a viscous fluid.
10.
State Bernoulli's equation and name two of its applications.
Section D — Long Answer (5 marks)
1 × 5 = 5 marks
11.
State and explain Bernoulli's principle for streamline flow. Using it, explain how the lift on an aeroplane wing and the working of an atomiser arise from the relation between speed and pressure.
Answer Key
Section A — Multiple Choice Questions
- (B) less than the fluid's
- (B) $\text{Pa}\cdot\text{s}$
- (A) $F=6\pi\eta r v$
- (C) constant
- (C) Bernoulli's principle
Section B — Short Answer (2 marks)
- A body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.
- The constant maximum velocity a body attains when the net force on it (weight minus buoyancy and viscous drag) becomes zero.
- $v_2=\frac{A_1v_1}{A_2}=\frac{6\times4}{2}=12\ \text{m/s}$.
Section C — Short Answer (3 marks)
- At terminal velocity, weight $=$ buoyancy $+$ drag: $\frac{4}{3}\pi r^3\rho g=\frac{4}{3}\pi r^3\sigma g+6\pi\eta r v_t$, giving $v_t=\frac{2r^2(\rho-\sigma)g}{9\eta}$.
- $P+\frac{1}{2}\rho v^2+\rho gh=\text{const}$ along a streamline; applications: aeroplane lift, atomiser/sprayer, venturimeter, spin of a ball (any two).
Section D — Long Answer (5 marks)
- Bernoulli: $P+\frac{1}{2}\rho v^2+\rho gh=\text{const}$ along a streamline, so where speed is high, pressure is low. Over a wing the curved top makes air move faster, lowering pressure above and creating net upward lift. In an atomiser, fast air across the top of a tube lowers the pressure there, so atmospheric pressure pushes liquid up the tube to be sprayed.
Generated by Vidaara.org · Assignment VID-P11-09-BVB-01 · vidaara.org