Subject: Science

Every liquid has a tendency to push the object towards its surface called upthrust. When a stone is immersed in water, water tries to push the stone to its surface. During this process the stone will lose some of its weight because water is trying to push it upward. Similarly water also pushes your body upward when you throw yourself into swimming pool. So it is easier for you to swim. So the upthrust of water will be

**Upthrust = weight in air - weight in water.**

**Density and relative density:**

Density is a physical property of a matter. It can be defined as a ratio of mass per unit volume. The qualitative definition can be the measure of the relative heaviness of an object with constant volume. For example, rock is denser than a piece of paper though they occupy the same volume (differ in the quantity of mass occupied in the same volume).

Formula for measuring density is density= \(\frac{mass}{volume}\). Unit of density is kg/m^{3}

Relative density is the ratio of the density of the substance to the density of water at 4 degree Celsius. Relative density does not have aunit. According to the density of the liquid, upthrust differs. If the liquid has higher density then upthrust exerted by it increases. That is why an egg does not float on pure water but floats on salt water. With the addition of salt,we increase the density of water. Due to higher density,the egg floats.

- Every liquid has a tendency to push the object towards its surface called upthrust.
- Formula for measuring density is : density= \(\frac{mass}{volume}\). The unit of density is kg/m
^{3}. - The ratio of the density of the substance to the density of water at 4 degree Celsius with the same volume is called relative density.

- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.

When a liquid is placed in a container, it exerts force on the bottom as well as on the walls of the container. The force (weight) of the liquid on per unit area of the container is called the liquid pressure.

Depth of the liquid (h), density of liquid (d) and acceleration due to gravity (g) are the three factors that affect the pressure due to liquid contained in a vessel.

In this case the tank with smaller base will exert more pressure because to contain same volume of liquid as the broad base tank the height of the tank with smaller base must be larger than the height of the tank with broader base. And according to the liquid pressure law as the height increases the pressure exerted by liquid increases.

The pressure due to liquid at the downstairs tap will be higher than the upstairs tap as according to liquid pressure law pressure exerted by liquid is directly proportional to height of the liquid column. Due to high pressure the water will flow with more force, at the lower tap, filling the bucket faster than the tap upstairs.

The pressure exerted by a liquid is directly proportional to the depth of the liquid, as we go deeper into the bottom the pressure increases. So withstand the large pressure at the bottom of the dam the wall in a dam is made comparatively thicker than at the surface. If the wall is thin then the risk of dam break is higher.

The height (h) of the blood column at the feet is large as compared to at the brain . Hence, blood pressure is more at feet that at the brain according to this formula, p=hdg where d = density of the medium(blood).

Study the diagram and answer the following question.

- What is the weight of an object in the air?
- How much upthrust is exerted by the liquid on that object?
- Calculate the mass of the object.

Solution,

Weight of body in liquid= 10N

Weight of displaced liquid= 2N

Weight of body in air=?

Using formula,

Weight of body in air= weight of body in liquid+ weight of displaced liquid

= 10+2

=12N

Upthrust= Weight of displaced liquid

= 2N

For mass of body,

Weight of body in air(W)=12N

Acceleration due to gravity= 10m/s^{2}

Mass of the body (m)=?

Using formula,

\begin{align*}m &=\frac{W}{g}\\ &= \frac{12}{10}\\&=1.2 \: kg. \end{align*}

The weight of a piece of stone, when immersed in water is 9N and it displaces 2N of water. Answer the following questions.

What is the weight of stone in the air?

Here,

Weight of stone in water= 9N

Weight of displaced water= 2N

Weight of stone in air=?

We know,

The weight of stone in air= Wt. of stone in water+ Wt. of displaced water

=9N +2N

=11N

The weight of a stone when immersed in water is 40N and it displaces 10N of water, Answer the following questions.

- What will be the upthrust of water?
- What is the weight of stone in the air?

Solution,

Upthrust of water=Weight of displaced water

=10N

Now,

Weight of stone in water=40N

Weight of displaced water =10N

Weight of stone in air=Wt. of stone in air+ Wt. of displaced water

=40N + 10N

= 50N

A piece of iron weighed 20N in air. If it weighs 12N when it is completely immersed in water. What is the weight of water displaced by iron and what is the upthrust in the iron?

Here,

The weight of iron in air= 20N

The weight of iron in water= 12N

The weight of water displace by iron= ?

we know,

The weight of water displaced by iron=wt of iron in air- wt of iron in water

=20N-12N

=8N

The upthrust on the iron= weight of displaced water = 8N

Upthrust = Wt. of displaced water

∴8N=8N

A stone hanging in a spring balance when dipped in water it displaces 5N water and the spring balance shows the reading of 3N. Calculate the upthrust and weight of the stone in air.

Here,

Wt. of stone in water= 3N

Wt. of displaced water= 5N

we know that,

The wt. of stone in air= Wt. of stone in water+wt. of displaced water

=3N+ 5N

=8N

Again,

Upthrust= Weight in air- Weight in water

=8N-3N

=5N

Hence, upthrust of water is 5N and the weight of stone in air is 8N.

A. A solid object weight 34N in air and 10N in water . What is the upthrust and weight of the liquid displaced ?

Here,

Weight of the object in air (W_{a}) =34N

Weight of the object in water (W_{w}) =10N

Upthrust = ?

Weight of the water displaced (W_{2}) =?

We know that,

Upthrust = W_{a}-W_{w}

= 34-10

= 24N

Again,

We know,

Upthrust (U) = Weight of the liquid displaced(W_{2})

∴ the weight of the liquid displaced =24N

Thus, upthrust on the body is 24N and weight of displaced fluid is 24N.

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