Option 4 : Surface Tension

__Concept:__

- Capillary action: If one end of a capillary tube is put into a liquid that wets glass, it is found that the liquid rises into the capillary tube to a certain height.
- This rise is due to inward pull of surface tension acting on the surface which pushes the liquid into the capillary tube.

The height of the liquid rises or fall (h) is given by

\({\rm{h}} = \frac{{4{\rm{\;T}}\cos {\rm{\theta }}}}{{{\rm{d\;\rho \;g}}}}\)

Where T = surface tension, θ = angle of contact, d = diameter of capillary tube, ρ = density of liquid, g = acceleration due gravity.

__Explanation__:

Hence the rise in capillary action is due to surface tension.

Option 4 : 760 Torr

__ CONCEPT__:

- Atmospheric pressure: The force per unit area pushed on any surface by the Earth's atmosphere is called atmospheric pressure.
- Atmospheric pressure decreases with an increase in the altitude for any region.
- This is because high altitude places do not have sufficient air above them, pushing down.
- Barometers used to measure the pressure of the atmosphere.

The **atmospheric pressure** is given by:

P = ρ g h

Where ρ is the density of the fluid/air, g is the acceleration due to gravity and h is the height of the fluid/air.

- The
**standard atmospheric pressure (1 atm)**is equal to the pressure which supports the 760 mm column of mercury at 0 °C at sea level. - The atmospheric pressure at sea level is equal to the atmospheric pressure on the earth's surface.

The value of **1 atm** is given by:

P = 1.013 x 10^{5} Pa = 1013 hPa = 1013 mb = 1 atm = 760 torr.

__ EXPLANATION__:

- The
**atmospheric pressure near the surface of the Earth is 760 Torr.**So option 4 is correct.

__ EXTRA POINTS__:

- Factors responsible for Atmospheric pressure:
- There are some major factors that are usually responsible for atmospheric pressure, which as follows:

- Altitude:
- Altitude means actual height above the sea level or above it may be above the plain ground.
- Altitude is used in general in aviation, especially in parachuting, flying, gliding, and surveying also it is used.
- In geometry, it is termed the height of the substance.

- Relation of Atmospheric pressure with Altitude:
- Atmospheric pressure
**decreases**with an increase in the altitude for any region. - The pressure at any geographical level in the atmosphere may be cumulated as the total weight of the air above one unit area.
- At higher altitudes, there are a few molecules of air above a specified surface than a similar surface of lower levels.

- Atmospheric pressure
- Earth's Rotation:

- The earth's rotation affects the pressure of the atmosphere in various ways.
- This happens because of the rotation swelling to the near of our equator.
- The rotation causes a displacement of fluid especially in the hemisphere, which converted to the clockwise direction, is called the Coriolis effect.

Option 3 : low density

__CONCEPT__:

**Cloud**is a**mass of minute water droplets or tiny crystals of ice formed by the condensation of the water vapour**in free air at considerable elevations.- As the clouds are formed at some height over the surface of the earth, they take various shapes.
- According to their
**height**,**expanse**,**density**, and transparency or opaqueness clouds are grouped under four types:- cirrus
- cumulus
- stratus

__EXPLANATION__:

**Clouds**are created when**water gets heated up**,**evaporates**, and**condenses**in the upper atmosphere.- The heating effect lifts up the
**air and**low pressure (or low density) is created over the area. Therefore option 3 is correct. - To fill the low pressure the air from the surroundings comes in to fill the void, and it also rises up.
- Thus constant upward air currents of air are created which keep the clouds floating in the sky.

Option 3 : Pascal's Law

__CONCEPT__:

- Pascal’s principle: Pascal’s Law is the principle of transmission of fluid-pressure.
- It says that "a pressure exerted anywhere in a point of the confined fluid is transmitted equally in all directions throughout the fluid”.

__EXPLANATION__:

- The statement,
**"The pressure in a fluid at rest is the same at all points if they are at the same height" represents pascal's law.**So option 3 is correct.

__Additional Information__

- Bernoulli's principle: For a streamlined flow of an ideal liquid in a varying cross-section tube the total energy per unit volume remains constant throughout the fluid.
- This means that in steady flow the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline.

- Archimedes' principle states that when a body immersed in a fluid, whether fully or partially submerged, the upward buoyant force that is exerted on it, is equal to the weight of the fluid that the body displaces.
- Boyle’s law: For a given mass of an ideal gas at a constant temperature, the volume of a gas is inversely proportional to its pressure.

i.e.\(\Rightarrow \frac{{{P_1}}}{{{P_2}}}\; = \;\frac{{{V_2}}}{{{V_1}}}\;\)

or PV = constant

⇒ P1V1 = P2V2

Option 4 : Buoyant Force

** CONCEPT**:

**Archimedes Principle:**The upward buoyant force that is exerted on a body immersed in a fluid, whether partially or fully submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the centre of mass of the displaced fluid.- The value of thrust force is given by the Archimedes law which was discovered by
**Archimedes of Syracuse of Greece**. When an object is partially or fully immersed in a liquid displaced by it. **Archimedes' principle**tells us that this loss of weight is equal to the weight of liquid the object displaces. If the object has a volume of V, then it displaces a volume V of the liquid when it is fully submerged. If only a part of the volume is submerged, the object can only displace that much liquid.

- The value of thrust force is given by the Archimedes law which was discovered by
**Archimedes Principle Formula:**In simple form, the Archimedes law states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. Mathematically written as:

F_{b} = ρ × g × V

Where** F _{b} is the buoyant force, ρ** is the

****__ EXPLANATION__:

- When a body partially and fully emerged in any fluid it experiences an upward force that is equal to the weight of the fluid displaced by it and it is called
**buoyant force**. - Hence option 4 is the correct answer.

Option 4 : Increases

**CONCEPT:**

- Ice is the
**solid state of water.** **Melting**is the process when the**solid is converted into liquid.**- In general, the solid-state is having more density than the liquid state of matter. But in the case of water, the
**liquid water is denser than solid.** - Ice is denser than water d
**ue to the crystalline structure of ice formed due to the orientation of hydrogen bonds.**This pushes the molecules of ice far apart.

**EXPLANATION:**

- So, when the ice melts, it is
**converted into liquid water.** - This liquid
**water is having more density than solid ice.** - So, overall
**ice melts its density Increases.** **'Increases'**is the correct answer.

Option 4 : surface tension

The correct answer is option 4) i.e. surface tension.

** CONCEPT**:

**Surface tension**is the tendency of water molecules to adhere to each other so as to form the**minimum surface area**possible.- This is a result of
**cohesion**between water molecules. - Towards the interface of water with air, there will be no cohesive forces. Hence the net force acts
**downwards**. - The top surface of the water will now act like a stretched membrane.

- This is a result of

** EXPLANATION**:

- When an iron needle is placed on water, the stretched membrane of water prevents the iron nail from sinking.
- The stretched membrane occurs due to the
**surface tension of water**.

**Hence, an iron needle floats on the surface of the water because of surface tension.**

__Confusion Points__

- Not all substances can float on water due to surface tension. Only objects whose weight is lesser than the force due to surface tension will float.
- The density of the iron needle is greater than that of water, but it does not sink because the weight is comparatively small to break the surface tension of the water surface.

Human hair cling together when it is removed from water due to

Option 2 : Surface tension

__CONCEPT:__

- The property of a liquid due to which its free surface tries to have the minimum surface area and behaves as if it were under tension somewhat like a stretched elastic membrane is called surface tension.
- The surface tension of a liquid is measured by the force acting per unit length on either side of an imaginary line drawn on the free surface of the liquid.

\(Surface\;tension = \frac{{Force}}{{length}}\)

__EXPLANATION:__

- When hair is dipped in water it spread out, but as soon as it is taken out, its sticks together are due to surface tension.
- This is caused because as we
**remove the hair from water, water molecules that are attached to hairs will try to reduce the surface area**because of cohesive force between them and this creates tension along the surface and hence hairs cling together.

Which of the following statements about a fluid at rest in a cup is/are correct?

1. Pressure is same at all the points in the fluid

2. Pressure is exerted on the walls

3. Pressure exists everywhere in the fluid

Option 2 : 2 and 3 only

__CONCEPT__

**Fluid Pressure:**Pressure P at every point in a fluid is defined as**the normal force per unit area**.

\(P = \frac{{d{{\vec F}_ \bot }}}{{dA}}\)

Where, P = pressure, d F = perpendicular force/normal force, d A = area

- The S.I unit of pressure is the
**Pasca**l,**1 Pascal = 1 N/m**^{2}

- Pressure at
**two-point in the horizontal plane**or same level when the fluid is at rest or uniform velocity is the**same.**

- Pressure at
**two-point at depth separation ‘h’**when fluid is at rest or uniform velocity is expressed by**P**_{2}– P_{1}= ρ × g × h - Where, P
_{2}and P_{1}are pressure at two different points, ρ = density of fluid, h = distance between them.

- The walls of the container always exert the force on the fluid.

__EXPLANATION__

According to the options,

**The pressure is same at all points in fluid**– This is**incorrect**as pressure is same in a horizontal position but not in the vertical position –**statement**1 is incorrect.**Pressure is exerted on the walls**– This is**correct**the pressure is exerted on the walls and from the walls to balance it –**statement**2 is correct.**Pressure exists everywhere in the fluid**– This is**correct**the pressure is everywhere in the fluid at some points they are same and some are not –**statement**3 is correct.

∴ **Option 2** is correct

Option 2 : Hydrometer

The correct answer is __ Hydrometer__.

__Key Points__

- The hydrometer basically consists of a weighted, sealed, long-necked glass bulb immersed in the measured liquid, the flotation depth shows the liquid density, and the neck can be calibrated to read the actual gravity value.
- A hydrometer used for determining the density of liquids is based on Archimedes' principle.

- Archimedes principle:
- It states that a body when wholly or partially immersed in liquid experiences an upward thrust which is equal to the volume of the liquid.
- Archimedes Principle is also known as the physical law of buoyancy.
- When a solid is fully immersed in a liquid, it loses weight, which is equal to the weight of the liquid it displaces.
**Apparent weight= actual weight−buoyant force= mg−ρgV****Where m = mass of the object and ρ = density of the fluid**

Option 2 : Dyne cm^{-1}

__Concept__:

Surface tension:

- Surface tension is the property by virtue of which liquid
**tries**to minimize its free surface area. - In spherical shape the surface area is minimum and for this reason, the raindrops are spherical.
- Surface tension is measured as the force acting per unit length of an imaginary line drawn on the liquid surface.

\(Surface\;tension = \frac{{Force}}{{length}}\)

Two factors can affect the surface tension of a liquid. The factors are-

- Temperature: If temperature increases then the surface tension of a liquid decreases.
- Soluble Impurities: In the case of less soluble impurities, the surface tension decreases. But, for highly soluble impurities in the liquid the surface tension increases.

**Explanation:**

we know that,

\(Surface\;tension = \frac{{Force}}{{length}}\)

**⇒ Dyne/cm or Dyne cm ^{-1}**

Option 2 : Energy

__CONCEPT:__

**Bernoulli's principle**: For a **streamlined flow of **an ideal liquid in a varying cross-section tube the **total energy per unit volume remains constant** throughout the fluid.

- This means that in
**steady flow the sum of all forms of mechanical energy**in a fluid along a**streamline is the same at all points**on that streamline.

From **Bernoulli's principle**

\(\frac{{{{\rm{P}}_1}}}{{\rm{\rho }}} + {\rm{g}}{{\rm{h}}_1} + \frac{1}{2}{\rm{v}}_1^2 = \frac{{{{\rm{P}}_2}}}{{\rm{\rho }}} + {\rm{g}}{{\rm{h}}_2} + \frac{1}{2}{\rm{v}}_2^2\)

\(\frac{{\rm{P}}}{{\rm{\rho }}} + {\rm{gh}} + \frac{1}{2}{{\rm{v}}^2} = {\bf{constant}}.\)

__EXPLANATION:__

- Bernoulli's principle is based on the
**principle of conservation of energy**. So at each point, the**net energy is conserved in the fluid**. So option 2 is correct.

**Areophane’s wings**are based on**Bernoulli's principle**so that**they can fly**.

Option 1 : Surface Tension

__CONCEPT:__

- Capillary action: If one end of a capillary tube is put into a liquid that wets glass, it is found that the liquid rises into the capillary tube to a certain height.
- This rise is due to inward pull of surface tension acting on the surface which pushes the liquid into the capillary tube.
- When the intermolecular interaction of the solvent itself is significantly inferior to the surface of the material it interacts with, capillary action occurs.
- It happens only when the binding forces in the liquid are greater than the cohesive forces, which inevitably develop into surface tension.

The height of the liquid rises or fall (h) is given by

\({\rm{h}} = \frac{{2{\rm{\;T}}\cos {\rm{\theta }}}}{{{\rm{d\;\rho \;g}}}}\)

Where T = surface tension, θ = angle of contact, d = diameter of capillary tube, ρ = density of liquid, g = acceleration due gravity.

__ EXPLANATION__:

**The capillary action**happens due to**Surface Tension.**So option 1 is correct.

Option 2 : 1/3

__ CONCEPT__:

- Archimedes' principle states that when a body immersed in a fluid, whether fully or partially submerged, the
**upward buoyant force**that is exerted on it,**is equal to the weight of the fluid that the body displaces**.

Fbuoyant = ρf Vf g

where ρf is the density of the fluid in which the object is submerged, Vf is the volume of the displaced fluid (or volume of the object that is submerged inside the fluid) and g is the gravitational acceleration.

**When an object is submerged in fluid fully or partially**there are two forces, 1. buoyant force 2. weight of the object/Gravitational force

Here **weight of object** (W) = mg = ρo Vo g

Where ρo is the density of the object, Vo is the volume of the object, g is the gravitational acceleration.

** CALCULATION**:

Given that:

The object floats in water with **one–third of its volume underwater**:

V_{f} = V_{0}/3

**According to Archimedes principle**:

Weight of the object (W) = Buoyancy force (F_{b})

So ρo Vo g = ρf Vf g

ρo Vo g = ρf (V_{0}/3) g

The** density of the object (ρo) = 1/3 × Density of fluid (ρ _{f})**

Option 2 : Hydraulic Lift

__CONCEPT:__

- Pascal’s principle: Pascal’s Law is the principle of transmission of fluid-pressure.
- It says that "a pressure exerted anywhere in a point of the confined fluid is transmitted equally in all directions throughout the fluid”.

__ EXPLANATION__:

**Centrifuge**: Centrifugation is used to separate the contents of mixtures according to their size and density. The**centrifuge works on the principle of sedimentation**.**Hydraulic Lift**: The lift that uses pascal's law and used to lift objects with the help of fluid is called hydraulic lift. It**works on Pascal's law. So option 2 is correct.**-
**Motor**: A motor is an electrical device that converts electrical energy into mechanical energy. It works on the**principle that a current-carrying conductor experiences a mechanical force**when it is placed in a magnetic field. **Lever**: A lever is a simple machine that is made up of two load arms and a fulcrum. The distance from the fulcrum can be used to determine how the input and output forces are related to each other.

Option 2 : Viscosity

__CONCEPT:__

- Viscous force (F): When a layer of fluid slips or tends to slip on adjacent layers in contact, the two layers exert tangential force on each other which tries to oppose the relative motion between them.
- The property of a fluid due to which it opposes the relative motion between its different layers is called viscosity (or fluid friction or internal friction) and the force between the layers opposing the relative motion is called viscous force.

- The force acting between the different layers of a fluid is given by:

\(F = - \eta A\frac{{dv}}{{dx}}\)

Where η = coefficient of viscosity, A = area of the plane and dv/dx = velocity gradient.

- A negative sign is employed because viscous force acts in a direction opposite to the flow of liquid.

__EXPLANATION:__

- When a liquid kept in a bucket is
**stirred for a few seconds and then kept at rest**, then the**liquid comes to rest**after some time due to**viscosity**because**different layers of liquid in a bucket oppose the relative motion**. Therefore option 2 is correct.

Option 3 : Density

__ CONCEPT__:

**Pressure (P):**The force per unit area is called pressure.- The SI unit of pressure is the pascal (Pa).

Pressure (P) = Force (F)/ Area (A)

**Force (F)**: The interaction that changes the state of rest or state of motion of a body is called force.- The SI unit of force is Newton (N).

Force (F) = Mass (m) × acceleration (a)

**Density (ρ):**The mass per unit volume is called density.- The SI unit of Density is Kilogram per cubic meter (kg/m
^{3}).

- The SI unit of Density is Kilogram per cubic meter (kg/m

Density (ρ) = Mass (m)/Volume (V).

__ EXPLANATION__:

**Mass/Volume = Density.**

So option 3 is correct.

Option 1 : Energy

__CONCEPT:__

Bernoulli's principle: For a streamlined flow of an ideal liquid in a varying cross-section tube the total energy per unit volume remains constant throughout the fluid.

This means that in steady flow the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline.

From Bernoulli's principle

\(\frac{{{{\rm{P}}_1}}}{{\rm{\rho }}} + {\rm{g}}{{\rm{h}}_1} + \frac{1}{2}{\rm{v}}_1^2 = \frac{{{{\rm{P}}_2}}}{{\rm{\rho }}} + {\rm{g}}{{\rm{h}}_2} + \frac{1}{2}{\rm{v}}_2^2\)

\(\frac{{\rm{P}}}{{\rm{\rho }}} + {\rm{gh}} + \frac{1}{2}{{\rm{v}}^2} = {\bf{constant}}.\)

__EXPLANATION:__

Bernoulli's principle is based on the principle of conservation of energy. So at each point, the net energy is conserved in the fluid.

Option 4 : Flow of a liquid

__CONCEPT__:

- The
**property of a liquid**due to which its**free surface**tries to have the**minimum surface area**and behaves as if it were under**tension**somewhat like a**stretched elastic membrane**is called**surface tension**. **The surface tension**of a liquid is measured by the**force acting per unit length**on either side of an imaginary line drawn on the free surface of the liquid i.e.- \(Surface\;tension = \frac{{Force}}{{length}}\)

__EXPLANATION__:

**Surface tension**is the result of the**cohesive force**among the**liquid molecules**, which always tries to make the**surface area of the liquid droplet minimum**.- Hence
**due to exertion of surface tension by the molecules, water droplets always take a round shape**whenever they are allowed to move freely and thus because of this we**see a**nearly**spherical drop of rain**. - The
**oil**and**grease****spots**on clothes cannot be removed by pure water. On the other hand, when**detergents (like soap)**are added in water, the**surface tension**of**water decreases**. As a result of this, the**wetting power**of**soap solution increases**. Also the**force of adhesion**between**soap solution and oil or grease**on the clothes**increases**. Thus, oil, grease, and dirt particles get mixed with soap solution easily. Hence clothes are washed easily. - The
**cohesive forces**are responsible for**surface tension between liquid molecules****and wall of**container hence along the wall of the surface liquid is more bound and rises above compared to centre this is known as capillary action which cause**Capillary rise** - Hence only option 4 is not a result of surface tension among all.

**Surface tension**of all**lubricating oils and paints**is**kept low**so that they**spread over a large area**.

Option 3 : Gases exhibit a large variation in densities with pressure.

__CONCEPT__:

- Density: The mass per unit volume is called density. It is denoted by ρ.
- The density of ice is less than that of water.
- The
**SI unit of density is kg/m**.^{3} - It is a scalar quantity.

Density (ρ) = Mass (M)/Volume (V)

**Relative density (RD)**: The ratio of the density of a material to the density of reference material (water) is called relative density.- It is a
**dimensionless quantity (No unit)**.

- It is a

**RD** = Density of a material/Density of reference material

__EXPLANATION__:

- Since
**relative density**is unitless. So statement 1 is wrong. **Liquids are not easily compressible**. So statement 2 is wrong.- Since the molecules of the gases are far apart from each other. So the
**gases exhibit a large variation in densities with pressure**. Hence option 3 is correct. - Density is a
**scalar quantity**.