Numericals On Upthrust Class 9 Worksheet

Numericals On Upthrust Class 9 Worksheet

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Upthrust, also known as buoyant force, is the force exerted by a fluid on an object immersed in it. This force acts opposite to gravity and is responsible for making objects appear lighter in water. The concept of upthrust is governed by Archimedes’ Principle, which states:

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

In this topic, we will explore important formulas, numerical problems, and solutions related to upthrust. These problems will help Class 9 students build a strong foundation in fluid mechanics.

Understanding Upthrust and Archimedes’ Principle

1. What is Upthrust?

Upthrust is the force exerted by a liquid or gas on an object placed in it. This force:

  • Acts vertically upwards

  • Opposes the weight of the object

  • Increases with density of the fluid

2. Formula for Upthrust

The buoyant force (upthrust, F_b ) is calculated as:

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)

3. Conditions for Floating and Sinking

  • If upthrust is greater than weight, the object floats.

  • If upthrust is equal to weight, the object remains suspended.

  • If upthrust is less than weight, the object sinks.

Numericals on Upthrust (Class 9 Worksheet)

Example 1: Finding Upthrust on a Submerged Object

Problem:
A wooden block of volume 0.02 m³ is fully submerged in water. Find the upthrust acting on it. Given:

  • 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) (0.02) (9.8)
F_b = 196 text{ N}

Final Answer: Upthrust = 196 N

Example 2: Checking If an Object Floats

Problem:
A metal block of mass 500 g and volume 4.5 à— 10⁻⁵ m³ is placed in water. Will it float or sink?

Solution:

Step 1: Find the weight of the block

W = mg
W = (0.5) (9.8) = 4.9 text{ N}

Step 2: Find upthrust using the formula

F_b = rho_f V g
F_b = (1000) (4.5 times 10^{-5}) (9.8)
F_b = 0.44 text{ N}

Step 3: Compare weight and upthrust

  • Weight = 4.9 N

  • Upthrust = 0.44 N

Since weight is greater than upthrust, the object will sink.

Final Answer: The metal block sinks.

Example 3: Volume of Displaced Water

Problem:
A plastic ball of mass 0.3 kg is floating in water. If its density is 600 kg/m³, find the volume of water displaced.

Solution:

Step 1: Find volume of the ball

V_{text{ball}} = frac{m}{rho}
V_{text{ball}} = frac{0.3}{600} = 5 times 10^{-4} text{ m³}

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

V_{text{displaced}} = 5 times 10^{-4} text{ m³}

Final Answer: Volume of displaced water = $5 times 10^{-4}$ m³

Example 4: Finding Density of a Floating Object

Problem:
A wooden cube of mass 250 g floats in water with half of its volume submerged. Find its density.

Solution:

Step 1: **Let total volume be V **

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

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

Step 2: Upthrust = Weight of object

rho_f V_{text{displaced}} g = mg
(1000) left( frac{V}{2} right) (9.8) = (0.25) (9.8)
frac{1000V}{2} = 0.25
500V = 0.25
V = frac{0.25}{500} = 5 times 10^{-4} text{ m³}

Step 3: Find density

rho = frac{m}{V}
rho = frac{0.25}{5 times 10^{-4}}
rho = 500 text{ kg/m³}

Final Answer: Density of wood = 500 kg/m³

Real-Life Applications of Upthrust

1. Ships and Boats

Ships float because their overall density is lower than water. The hollow design allows them to displace more water, creating a large upthrust.

2. Submarines

Submarines control their depth by adjusting the amount of water in ballast tanks, changing their buoyancy.

3. Hot Air Balloons

Air inside the balloon is heated to become less dense, creating an upthrust that lifts the balloon.

4. Swimming and Diving

Humans float when they displace enough water. Wearing life jackets increases upthrust, making it easier to stay afloat.

Tips for Solving Upthrust Numericals

  1. Convert all units properly (grams to kg, cm³ to m³).

  2. Use the correct density values for water ( $1000$ kg/m³).

  3. Understand when to use weight and upthrust formulas.

  4. For floating objects, upthrust = weight.

  5. If an object sinks, its weight is greater than the upthrust.

Common Mistakes to Avoid

  • Forgetting to convert mass to kg when calculating weight.

  • Using the wrong volume (total vs. displaced).

  • Not applying Archimedes’ Principle correctly in floating problems.

  • Mixing density of the object and density of the fluid.

Understanding upthrust and buoyancy is essential for Class 9 physics. By practicing numerical problems, students can grasp the concept of Archimedes’ Principle and its real-world applications. These principles help explain floating ships, swimming, submarines, and many daily-life experiences.

With regular practice and conceptual clarity, solving upthrust numericals becomes easier, preparing students for exams and higher-level physics.