Class 9 Upthrust in Fluids, Archimedes' Principle and Floatation Mock Test (ICSE)

Topics in Upthrust in Fluids, Archimedes' Principle and Floatation

• Upthrust and its cause
• Archimedes' principle
• Relative density and its determination
• Principle of floatation
• Applications of floatation

Upthrust in Fluids, Archimedes' Principle and Floatation practice questions with answers

1. Q1Multiple choice·1 mark
   A solid body of volume $V$ is completely immersed in a liquid of density $\rho$. The magnitude of the upthrust experienced by the body is given by:

   1. (a)$\frac{\rho g}{V}$
   2. (b)$V\rho g$
   3. (c)$V g / \rho$
   4. (d)$\frac{V\rho}{g}$
   Show answer and step marks

   1. Correct option: (b) $V\rho g$+1

   Answer: (b)
2. Q2Multiple choice·1 mark
   A wooden block floats in water with half of its volume submerged. What is the relation between the density of wood ($\rho_w$) and the density of water ($\rho_0$)?

   1. (a)$\rho_w = 0.5\rho_0$
   2. (b)$\rho_w = 0.25\rho_0$
   3. (c)$\rho_w = \rho_0$
   4. (d)$\rho_w = 2\rho_0$
   Show answer and step marks

   1. Correct option: (a) $\rho_w = 0.5\rho_0$+1

   Answer: (a)
3. Q3Multiple choice·1 mark
   Why does an iceberg float in seawater with a large portion submerged inside water?

   1. (a)Density of ice is slightly less than that of seawater.
   2. (b)Upthrust on the iceberg is greater than the weight of the iceberg.
   3. (c)Density of ice is equal to the density of seawater.
   4. (d)Density of ice is much less than that of seawater.
   Show answer and step marks

   1. Correct option: (a) Density of ice is slightly less than that of seawater. A floating body sinks until the upthrust equals its weight; since ice is only slightly less dense than seawater, about nine-tenths of the iceberg must be submerged.+1

   Answer: (a)
4. Q4Multiple choice·1 mark
   The relative density of a substance is $2.5$. Its density in SI units is:

   1. (a)$2.5 \times 10^2\text{ kg m}^{-3}$
   2. (b)$2.5 \times 10^3\text{ kg m}^{-3}$
   3. (c)$2.5\text{ kg m}^{-3}$
   4. (d)$25\text{ kg m}^{-3}$
   Show answer and step marks

   1. Correct option: (b) $2.5 \times 10^3\text{ kg m}^{-3}$+1

   Answer: (b)
5. Q5Long answer·4 marks
   (a) State Archimedes' principle. (b) A solid piece of iron of mass $160\text{ g}$ and density $8\text{ g/cm}^3$ is completely immersed in water. Calculate the upthrust acting on the iron piece. (Take density of water = $1\text{ g/cm}^3$ and $g = 10\text{ m/s}^2$)
   Show answer and step marks

   1. State Archimedes' principle correctly: When a body is partially or wholly immersed in a fluid, it experiences an upward force (upthrust) which is equal to the weight of the fluid displaced by it.+1
   2. Volume of the iron piece $V = \frac{\text{mass}}{\text{density}} = \frac{160\text{ g}}{8\text{ g/cm}^3} = 20\text{ cm}^3 = 2 \times 10^{-5}\text{ m}^3$.+1
   3. Substitution in upthrust formula: Upthrust $F_b = V \times \rho_{\text{water}} \times g = 2 \times 10^{-5}\text{ m}^3 \times 1000\text{ kg/m}^3 \times 10\text{ m/s}^2$.+1
   4. Final evaluation with correct unit: Upthrust = $0.2\text{ N}$ (or $20\text{ gf}$).+1

   Answer: (a) When a body is partially or wholly immersed in a fluid, it experiences an upthrust equal to the weight of the fluid displaced by it. (b) Upthrust $= 0.2\text{ N}$ (or $20\text{ gf}$).
6. Q6Long answer·4 marks
   A solid iron piece of mass $160\text{ kg}$ and volume $0.02\text{ m}^3$ is completely immersed in water of density $1000\text{ kg m}^{-3}$. Take acceleration due to gravity $g = 10\text{ m s}^{-2}$. (a) State Archimedes' principle. (b) Calculate the upthrust experienced by the iron piece. (c) Calculate the apparent weight of the iron piece in water.
   Show answer and step marks

   1. (a) State Archimedes' principle: When a body is partially or wholly immersed in a fluid, it experiences an upthrust (buoyant force) which is equal to the weight of the fluid displaced by it.+1
   2. (b) Formula for upthrust: $F_B = V \times \rho \times g = 0.02 \times 1000 \times 10 = 200\text{ N}$.+1.5
   3. (c) Real weight $W = m \times g = 160 \times 10 = 1600\text{ N}$. Apparent weight = Real weight $-$ Upthrust = $1600\text{ N} - 200\text{ N} = 1400\text{ N}$.+1.5

   Answer: (a) When a body is partially or wholly immersed in a fluid, it experiences an upthrust equal to the weight of the fluid displaced by it. (b) Upthrust $= 200\text{ N}$. (c) Apparent weight $= 1400\text{ N}$.

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