Numericals On Upthrust For Class 9

Numericals On Upthrust For Class 9

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Upthrust, also known as buoyant force, is a crucial concept in physics, particularly in fluid mechanics. It explains why objects float or sink when placed in a liquid. This principle is widely applied in daily life, from ships floating on water to submarines adjusting their depth.

In this topic, we will discuss important formulas, solved numerical problems, and key concepts related to upthrust. These numericals are designed to help Class 9 students understand and apply Archimedes’ Principle effectively.

Understanding Upthrust and Buoyant Force

1. What is Upthrust?

Upthrust is the upward force exerted by a liquid or gas on an object immersed in it. It works against gravity, making objects appear lighter in water than in air.

2. Archimedes’ Principle

The principle states:

“When an object is fully or partially submerged in a fluid, it experiences an upward force equal to the weight of the displaced fluid.”

This principle is key to understanding why objects float or sink.

3. Formula for Upthrust

The buoyant force ( F_b ) is given by:

F_b = rho_f V g

where:

  • F_b = Buoyant force (N)
  • rho_f = Density of the fluid (kg/m³)
  • V = Volume of displaced fluid (m³)
  • g = Acceleration due to gravity (9.8 m/s²)

Numerical Problems on Upthrust (Class 9)

Example 1: Finding the Upthrust on a Submerged Object

Problem:
A solid block of volume 0.03 m³ is completely submerged in water. Calculate the upthrust acting on it.

  • Density of water = $1000$ kg/m³
  • Acceleration due to gravity = $9.8$ m/s²

Solution:

Using the formula:

F_b = rho_f V g
F_b = (1000) (0.03) (9.8)
F_b = 294 text{ N}

Final Answer: The upthrust is 294 N.

Example 2: Will the Object Float or Sink?

Problem:
A wooden block has a mass of 600 g and a volume of 0.001 m³. Will it float in water?

Solution:

Step 1: Find the weight of the block

W = mg
W = (0.6) (9.8) = 5.88 text{ N}

Step 2: Find the upthrust

F_b = rho_f V g
F_b = (1000) (0.001) (9.8)
F_b = 9.8 text{ N}

Step 3: Compare Weight and Upthrust

  • Weight of block = 5.88 N
  • Upthrust = 9.8 N

Since upthrust is greater than weight, the block will float.

Final Answer: The wooden block will float.

Example 3: Volume of Water Displaced by a Floating Object

Problem:
A plastic ball of mass 0.4 kg is floating in water. If its density is 500 kg/m³, find the volume of water displaced.

Solution:

Step 1: Find the volume of the ball

V_{text{ball}} = frac{m}{rho}
V_{text{ball}} = frac{0.4}{500} = 8 times 10^{-4} text{ m³}

Step 2: For a floating object, volume of displaced water = volume of object submerged

Since the object is floating, it displaces its own weight in water.

V_{text{displaced}} = 8 times 10^{-4} text{ m³}

Final Answer: Volume of displaced water is $8 times 10^{-4}$ m³.

Example 4: Finding the Density of a Floating Object

Problem:
A wooden cube of mass 300 g floats in water with half of its volume submerged. Find its density.

Solution:

Step 1: **Let the total volume of the cube be V **

Since half of it is submerged, the volume of displaced water is:

V_{text{displaced}} = frac{V}{2}

Step 2: Using Archimedes’ Principle

rho_f V_{text{displaced}} g = mg
(1000) left( frac{V}{2} right) (9.8) = (0.3) (9.8)
frac{1000V}{2} = 0.3
500V = 0.3
V = frac{0.3}{500} = 6 times 10^{-4} text{ m³}

Step 3: Find the density

rho = frac{m}{V}
rho = frac{0.3}{6 times 10^{-4}}
rho = 500 text{ kg/m³}

Final Answer: Density of the wood is 500 kg/m³.

Applications of Upthrust in Daily Life

1. Floating of Ships

Ships are designed to displace large volumes of water, creating sufficient upthrust to keep them afloat.

2. Working of Submarines

Submarines adjust their buoyancy by filling or emptying ballast tanks with water or air.

3. Swimming and Life Jackets

People float better when they wear life jackets, which increase buoyant force by displacing more water.

4. Hot Air Balloons

Instead of water, hot air balloons use air buoyancy to float. Hot air inside the balloon is less dense than the surrounding air, creating upthrust.

Tips for Solving Upthrust Numericals

  1. Always convert mass to kilograms (kg) and volume to cubic meters (m³).
  2. Remember: Upthrust = weight of displaced fluid.
  3. If an object floats, upthrust equals weight.
  4. Compare upthrust with weight to determine if an object will float or sink.
  5. For fully submerged objects, volume of object = volume of displaced liquid.

Common Mistakes to Avoid

  • Forgetting unit conversions (grams to kg, cm³ to m³).
  • Confusing density of fluid with density of object.
  • Not applying the correct formula for upthrust.
  • Incorrectly identifying displaced volume for floating objects.

Understanding upthrust and buoyancy is essential for Class 9 physics students. By practicing numerical problems, students can grasp the applications of Archimedes’ Principle in real life, from floating ships to swimming techniques.

Regular practice and conceptual clarity will make upthrust numericals easier to solve, ensuring a strong foundation in fluid mechanics.