Class 10 Pressure Exercise 8.1 Solutions | Science and Technology Curriculum Development Centre

From the given figure, we can note the following:

• Weight of cork in the air (Wa) = 4 N
• Weight of cork in liquid (Wb) = 1 N
• Weight of liquid displaced (Wc) = (Wa - Wb) = 3 N

According to Archimedes' Principle, the upthrust due to water on an object that is partially or wholly immersed in a fluid is equal to the weight of liquid displaced by the object.

Hence, upthrust (U) = Wc = 3 N

The required upthrust when the cork is placed in the liquid is 3 N.

Differences between Pressure and Upthrust are:

The steel pin sinks in the water because its density is greater than that of water.

However, the steel's density is less than that of water causing it to float on water.

Any object that has a density more than the solution sinks in it. If its density is less than the solution or liquid, it floats on it. These are the cases of the law of floatation.

Balloon rising: When the air inside the balloon is heated it expands, due to which its density decreases and the surrounding cold air has more density. 

Because the hot air is less dense, the buoyant force acting on the balloon due to the difference in density between the heated air inside and the cooler air outside becomes greater than the weight of the balloon.

As a result, when the buoyant force exceeds the gravitational force pulling down on the balloon, it rises into the air.

Balloon sinking: When the air inside the balloon while in air is cooled down the density of air inside the balloon increases. 

With denser air inside, the buoyant force acting on the balloon decreases. If this force falls below the weight of the balloon , it can no longer support it.

Consequently, when gravity overcomes buoyancy, the balloon begins to sink.

Special types of oil like mineral oil are used in hydraulic brakes. 

Nature of such oil listed below make them suitable for their use in hydraulic brakes:

1. Non-Hygroscopic: Oil used in hydraulic brakes don't absorb moisture from the air. This property helps maintain consistent brake performance, as moisture can lower the boiling point of brake fluid and lead to brake failure.
2. Compatibility with Seals: Such oil is less aggressive on rubber seals compared to other fluids. This compatibility extends the life of the seals, reducing the risk of leaks and maintaining effective braking 

When a wooden cork is pushed below the water's surface, it displaces a volume of water equal to its own volume, creating an upward buoyant force. While the finger applies downward force, the cork remains submerged. 

Once the finger is removed, the buoyant force exceeds the weight of the cork, causing it to rise to the surface.

 This phenomenon illustrates Archimedes' Principle, where the buoyant force acts on objects submerged in fluid.

When we are floating on water, our water and buoyant force on our body are equal or balanced because of which we feel lighter while floating on water.

When a stone is submerged in water, it experiences a buoyant force that counteracts its weight. This buoyant force makes the stone feel lighter while underwater.

 Upon lifting the stone out of the water, the buoyant force is removed, and only the stone's weight is felt. Consequently, it feels heavier when lifted out because the upward force from the water is no longer acting on it, revealing its true weight.

Thus, on lifting a stone submerged in water, it feels heavier when it comes out of the water.

The Dead Sea offers a greater upthrust on a body than does a swimming pool. Hence, it is easier to float in the Dead Sea than in a swimming pool.

Explanation

$\rm U \propto \rho$. The density of the Dead Sea (1240 $\rm kgm^{-3}$) is much greater than that of a swimming pool. Hence, the Dead Sea offers a greater upthrust than the water in a swimming pool.

A boat is designed in such a way that it displaces water equal to upthrust experienced by it causing it to float(Archimedes' principle). 

When more passengers climb onto a boat than its maximum capacity, the total weight of the boat increases. This added weight causes the boat to displace more water. 

If the displaced water's weight is less than the total weight of the boat and passengers, the buoyant force decreases.

Once the buoyant force is insufficient to counteract the boat's weight, it can no longer stay afloat, leading to the risk of sinking.

Pascal's law for liquid pressure states, “When a force is exerted on a liquid enclosed in a container, the liquid exerts pressure equally in all directions.”

Any two applications of Pascal's law in daily life are mentioned below:

1. Hydraulic lift: A hydraulic lift is used to lift heavy objects with minimum force. For example: a dentist uses a hydraulic lift to ascend/descend the height of the chair during the treatment.
2. Hydraulic brake: A hydraulic brake is utilized in automobiles to stop them immediately.

A hydraulic machine is a device that uses liquid to convert energy, typically employing pressurized fluid to perform work. 

It operates based on Pascal's Law, which states that pressure applied to a confined fluid is transmitted equally in all directions. This principle allows hydraulic machines to amplify force, making them effective for lifting heavy loads and performing various mechanical tasks.

Archimedes' principle states that “ When a body is immersed partially or completely in a liquid, it experiences an upthrust which is equal to the weight of the liquid displaced by it.”

When a body is wholly or partially immersed in water then the liquid exerts an upward acting force. The upward-acting force is called upthrust.

There are six weighing machines in the figures given above.

Water does not flow out of the container in the first set of three weighing machines. Hence, the readings shown by the weighing machine given in Figure (a) increases. The first reading is 20 N. The second reading is 25 N and the final reading is 28 N.

Water flows out of the container in the final set of three weighing machines. According to Archimedes' principle, upthrust is equal to the weight of water displaced. To support the 5N and 8N weights, water from the container flows out.

Therefore, the readings shown by the weighing machine given in Figure (b) are 30 N.

Let forces $\rm F_{A}$ and $\rm F_{B}$ are acting on the two pistons A and B, respectively. Similarly. let $\rm A$ and $\rm B$ be the surface area of each pistons.

Given,

$\rm F_{A} = 20 N$ and $\rm A = 0.5 cm^{2}$

$\rm F_{B} = ? N$ and $\rm B = 5 cm^{2}$

By Pascal's law of liquid pressure, we have

$\rm P_{A} = P_{B}$

$\rm or, \frac{ F_{A}}{A} = \frac{F_{B}}{B}$

$\rm or, F_{B} = \frac{ B}{A} \cdot F_{A}$

$\rm or, F_{B} = \frac{ 5}{0.5} \cdot 20 N$

$\rm \therefore F_{B} = 200N$

Hence, the required force to be applied through syringe B to balanced the force on piston A is 200 N.

Given

Pressure (P) = 30 000 $\rm Pa$

Area (A) = 0.1 $\rm m^2$

To find: Force (F) = ? $\rm N$

By the Pressure Formula, we have,

$\rm P = \frac{F}{A}$

$\rm or, F = P \cdot A$

$\rm or, F = 30 000 \cdot 0.1$

$\rm \therefore F = 3 000 N$

Hence, the given hydraulic lift can lift a maximum load of 3,000 N.

Reason

A hydraulic lift is based on Pascal's law. According to this law, liquid enclosed in a container exerts equal pressure in all directions.