Angle of Contact Questions in English

(B) liquid does not wet the solid surface if the angle of contact is obtuse,i.e.,greater than $90^{\circ}$.
In this case,the cohesive forces between the liquid molecules are greater than the adhesive forces between the liquid and the solid surface.
Consequently,the liquid does not spread over the surface and does not wet it.

(A) The correct answer is $A$ (Convex).
The shape of the meniscus is determined by the relative strengths of cohesive forces (forces between liquid molecules) and adhesive forces (forces between liquid molecules and the container surface).
For mercury,the cohesive forces between mercury atoms are significantly stronger than the adhesive forces between mercury atoms and the glass surface of the capillary tube.
Because the cohesive forces dominate,the mercury atoms tend to pull away from the glass walls and towards each other,resulting in a convex meniscus shape.

(B) The angle of contact $\theta$ is determined by the balance of surface tension forces at the interface of liquid,solid,and gas.
As the temperature increases,the cohesive forces between the liquid molecules decrease more rapidly than the adhesive forces between the liquid and the solid surface.
Since the angle of contact is inversely related to the strength of the adhesive forces relative to the cohesive forces,a reduction in cohesive force leads to a decrease in the angle of contact.
Therefore,the correct option is $(b)$.

(D) The angle of contact is defined as the angle between the tangent to the liquid surface at the point of contact and the solid surface inside the liquid.
For liquids that do not wet the solid surface,such as mercury in contact with glass,the angle of contact is obtuse.
The angle of contact for the glass-mercury interface is approximately $135^o$ to $140^o$.
Among the given options,$135^o$ is the correct value.
Therefore,the correct option is $D$.

(B) The angle of contact is the angle between the tangent to the liquid surface at the point of contact and the solid surface inside the liquid.
For a liquid that does not wet the solid surface,the cohesive forces between liquid molecules are stronger than the adhesive forces between the liquid and solid molecules.
In the case of mercury and glass,the angle of contact is approximately $135^\circ$ to $140^\circ$,which is an obtuse angle.
Because the angle of contact is obtuse,the mercury drop tends to minimize its contact area with the glass,causing it to remain as a drop rather than spreading.

(D) The angle of contact between a liquid and a solid surface determines whether the liquid will wet the surface or not.
If the angle of contact is less than $90^\circ$,the liquid wets the surface.
If the angle of contact is greater than $90^\circ$,the liquid does not wet the surface.
Chromium is used for polishing motor car parts because it is water-repellent,meaning it prevents water from sticking to the surface and causing corrosion.
Therefore,the angle of contact between water and chromium must be greater than $90^\circ$.

(B) The angle of contact is a characteristic property of the pair of materials in contact (in this case,glass and mercury) and the surrounding medium.
It depends on the nature of the liquid and the solid surface,as well as the temperature.
It does not depend on the orientation or the inclination of the solid surface relative to the liquid surface.
Therefore,if the glass plate is inclined,the angle of contact will remain unchanged.

(A) convex meniscus occurs when the cohesive forces between liquid molecules are stronger than the adhesive forces between the liquid and the container wall.
This typically happens when mercury is placed in a glass capillary tube.
In a convex meniscus,the angle of contact $\theta$ is defined as the angle between the tangent to the liquid surface and the solid surface,measured inside the liquid.
For a convex meniscus,this angle of contact is always greater than $90^{\circ}$.

(C) When a water drop is placed between two glass plates,the water wets the glass surface because the angle of contact between water and glass is acute (less than $90^{\circ}$).
Due to surface tension,the liquid surface tends to minimize its area.
For a liquid that wets the surface (acute angle of contact),the meniscus becomes concave towards the air.
This results in the liquid spreading out and forming a concave shape between the two plates,as shown in image $52-$c10.

(A) The contact angle is defined as the angle between the tangent to the liquid surface at the point of contact and the solid surface inside the liquid.
For liquids that wet the solid surface,the contact angle is acute $(< 90^{\circ})$.
Kerosene is a liquid that wets most solid surfaces easily.
Experimental observations show that the contact angle for kerosene with a clean solid surface is $0^{\circ}$.

(C) The shape of the meniscus is determined by the angle of contact $\theta$ between the liquid and the solid surface.
For a liquid with an angle of contact $\theta = 0^{\circ}$,the adhesive forces between the liquid and the solid are very strong compared to the cohesive forces within the liquid.
This results in the liquid wetting the surface completely,causing the meniscus to curve into a semi-spherical shape.
Therefore,the correct answer is semi-spherical.

(B) When a liquid wets a solid completely,the adhesive forces between the liquid and solid molecules are stronger than the cohesive forces between the liquid molecules themselves.
This results in an angle of contact $\theta$ that is less than $90^{\circ}$.
For any liquid where the angle of contact $\theta < 90^{\circ}$,the shape of the meniscus in a capillary tube is concave.

(B) For a non-wetting liquid,the angle of contact $\theta$ is obtuse $(\theta > 90^{\circ})$.
Due to the cohesive forces being stronger than the adhesive forces,the liquid surface curves to form a convex meniscus.
Therefore,the shape of the meniscus is convex upward.

(B) The angle of contact depends on the nature of the liquid and the solid surface in contact.
Pure water and glass,as well as alcohol and glass,are both pairs where the liquid wets the solid surface.
In both cases,the adhesive force between the liquid and solid molecules is greater than the cohesive force between the liquid molecules.
Consequently,both pairs exhibit an acute angle of contact,making them the correct choice.

(D) The angle of contact is defined as the angle between the tangent to the liquid surface at the point of contact and the solid surface inside the liquid.
For a plane liquid surface,the tangent to the liquid surface at the point of contact is parallel to the wall of the container.
Therefore,the angle between the tangent and the wall is $0^\circ$.

(A) The height of the liquid column in a capillary tube is given by the formula $h = \frac{2T \cos \theta}{rdg}$,where $T$ is the surface tension,$\theta$ is the angle of contact,$r$ is the radius of the tube,$d$ is the density of the liquid,and $g$ is the acceleration due to gravity.
For the liquid to rise in the tube,the height $h$ must be positive.
Since $T, r, d,$ and $g$ are always positive,the sign of $h$ depends on $\cos \theta$.
If the angle of contact $\theta$ is acute (i.e.,$0^{\circ} \le \theta < 90^{\circ}$),then $\cos \theta$ is positive,making $h$ positive,which indicates a rise in the liquid level.
Therefore,the correct option is $A$.

(C) The wettability of a surface by a liquid is determined by the angle of contact $\theta$ between the liquid and the solid surface.
If the angle of contact $\theta$ is acute $(\theta < 90^{\circ})$,the liquid wets the surface.
If the angle of contact $\theta$ is obtuse $(\theta > 90^{\circ})$,the liquid does not wet the surface.
Therefore,the primary factor determining wettability is the angle of contact.

(B) Let the contact angle be $\theta$. Consider the center of the sphere $O$ and the point of contact $A$ at the edge of the liquid surface. Let $B$ be the point on the vertical axis at the same level as the liquid surface.
In the right-angled triangle $\Delta OBA$,the hypotenuse $OA = R$ (radius of the sphere).
The vertical distance from the center $O$ to the liquid surface is $R - h$.
Thus,$OB = R - h$.
The angle between the radius $OA$ and the vertical line $OB$ is $(90^{\circ} - \theta)$,where $\theta$ is the contact angle.
In $\Delta OBA$,we have:
$\cos(90^{\circ} - \theta) = \frac{OB}{OA} = \frac{R - h}{R}$
Since $\cos(90^{\circ} - \theta) = \sin \theta$,we have $\sin \theta = \frac{R - h}{R}$.
However,looking at the geometry,the angle between the tangent to the surface at $A$ and the radius $OA$ is $90^{\circ}$. The angle between the horizontal liquid surface and the radius $OA$ is $\theta$.
Therefore,$\cos \theta = \frac{OB}{OA} = \frac{R - h}{R}$.
Thus,$\theta = \cos^{-1} \left( \frac{R - h}{R} \right)$.

(A) Detergents are surfactants that lower the surface tension of water.
When detergent is added to water,it reduces the angle of contact between the cleaning solution and the glass surface.
$A$ smaller angle of contact allows the solution to spread more effectively over the surface and penetrate the grease,facilitating its removal.
Therefore,the correct reason is that it reduces the angle of contact.

(D) In a gravity-free environment,the shape of the liquid is determined by the minimization of surface energy. The total surface energy is the sum of the liquid-solid surface energy and the liquid-air surface energy. Since the contact angle is zero,the liquid perfectly wets the inner surface of the sphere. To minimize the total surface energy,the liquid will spread to cover the entire inner surface of the sphere,forming a spherical shell of liquid. This configuration maximizes the liquid-solid contact area (which is energetically favorable due to the zero contact angle) and minimizes the liquid-air surface area for a given volume. Therefore,the liquid will coat the inner surface of the sphere.

(B) The height of liquid rise in a capillary tube is given by the formula:
$h = \frac{2T \cos \theta}{r \rho g}$
Where $T$ is surface tension,$\theta$ is the angle of contact,$r$ is the radius of the tube,$\rho$ is the density of the liquid,and $g$ is the acceleration due to gravity.
When the level of the liquid inside and outside the capillary tube is the same,the height of the rise $h$ is $0$.
Substituting $h = 0$ into the formula:
$0 = \frac{2T \cos \theta}{r \rho g}$
Since $T$,$r$,$\rho$,and $g$ are non-zero constants,we must have:
$\cos \theta = 0$
This implies that $\theta = 90^{\circ}$.

(B) The shape of the meniscus in a capillary tube is determined by the angle of contact $\theta$ between the liquid and the solid surface.
If the liquid surface (meniscus) is hemispherical,it implies that the liquid perfectly wets the surface of the capillary tube.
For a hemispherical meniscus,the tangent to the liquid surface at the point of contact is vertical,which means the angle of contact $\theta$ is $0^o$.
Therefore,the correct option is $B$.

(N/A) The surface of a liquid near the plane of contact with another medium is curved.
Angle of contact: The angle between the tangent to the liquid surface at the point of contact and the solid surface inside the liquid is known as the angle of contact. It is denoted by $\theta$.
It varies for different pairs of liquids and solids.
In the figure,$(a)$ shows a water droplet on a lotus leaf,and $(b)$ shows water spreading over a clean plastic plate.
Let the surface tensions be:
$S_{la} = \text{surface tension of liquid-air interface}$
$S_{sa} = \text{surface tension of solid-air interface}$
$S_{sl} = \text{surface tension of solid-liquid interface}$
At the line of contact,the surface forces between the three media must be in equilibrium.
For figure $(a)$:
$S_{sa} = S_{sl} + S_{la} \cos \theta$
$\cos \theta = \frac{S_{sa} - S_{sl}}{S_{la}}$
If the cohesive forces between liquid molecules are stronger than the adhesive forces between liquid and solid molecules,then $S_{sl} > S_{sa}$,resulting in $\cos \theta < 0$,which means $\theta$ is obtuse. In this case,the liquid does not wet the solid surface,and the meniscus is convex.
If the adhesive forces are stronger than the cohesive forces,then $S_{sa} > S_{sl}$,resulting in $\cos \theta > 0$,which means $\theta$ is acute. In this case,the liquid wets the solid surface,and the meniscus is concave.

(N/A) The angle of contact is defined as the angle between the tangent to the liquid surface at the point of contact and the solid surface inside the liquid.
It is measured through the liquid.
For a liquid that wets the solid surface (e.g.,water and glass),the angle of contact is acute $(< 90^{\circ})$.
For a liquid that does not wet the solid surface (e.g.,mercury and glass),the angle of contact is obtuse $(> 90^{\circ})$.

(B) The wings of a duck are coated with a special oily secretion produced by glands in their body.
This oil makes the feathers hydrophobic,meaning they repel water.
In terms of surface tension,the angle of contact between the water and the oily surface of the feathers is obtuse $(> 90^{\circ})$.
Because the angle of contact is obtuse,the water does not spread over the feathers and instead forms droplets that roll off,preventing the wings from getting wet.

(A) $(i)$ When a liquid wets a solid surface (sticks to it),the adhesive forces between the liquid and solid molecules are stronger than the cohesive forces between the liquid molecules. This results in a concave meniscus,which corresponds to an acute angle of contact (less than $90^{\circ}$).
$(ii)$ Mercury does not wet glass because the cohesive forces between mercury atoms are much stronger than the adhesive forces between mercury and glass. This results in a convex meniscus,which corresponds to an obtuse angle of contact (greater than $90^{\circ}$,typically around $135^{\circ}-140^{\circ}$).

(A) When a liquid wets a solid surface,the adhesive forces between the liquid molecules and the solid surface are stronger than the cohesive forces between the liquid molecules themselves.
This results in the liquid spreading over the surface,causing the angle of contact to be acute (less than $90^{\circ}$).

(B) When a liquid does not wet the surface,the cohesive forces between the liquid molecules are stronger than the adhesive forces between the liquid and the solid surface.
This results in the liquid forming a convex meniscus.
For a convex meniscus,the angle of contact $\theta$ is always greater than $90^{\circ}$.
Therefore,the angle of contact is obtuse.

(N/A) The angle of contact depends on the following factors:
$(1)$ The nature of the liquid and the solid in contact.
$(2)$ The cleanliness of the contact surface of the solid.
$(3)$ The medium (e.g.,air or vapor) that exists above the free surface of the liquid.
$(4)$ The temperature of the liquid.

(A) The angle of contact $\theta$ depends on the surface tension of the liquid-solid interface,the liquid-air interface,and the solid-air interface. As the temperature of a liquid increases,its surface tension decreases. This change in surface tension affects the balance of forces at the point of contact,leading to an increase in the angle of contact $\theta$.

(N/A) Teflon is a polymer known as polytetrafluoroethylene $(PTFE)$.
It has a very low surface energy,which results in a high angle of contact between the surface of the pan and liquids like oil or water.
Because the angle of contact is obtuse $(> 90^{\circ})$,the adhesive forces between the liquid and the Teflon surface are much weaker than the cohesive forces within the liquid.
Consequently,the liquid does not wet or stick to the surface,making the pan non-stick.

(N/A) The angle of contact between water and the material of the raincoat is obtuse. Because the angle of contact is greater than $90^{\circ}$,the cohesive forces between water molecules are stronger than the adhesive forces between water and the raincoat material. Consequently,the water does not spread over the surface and instead forms droplets,preventing the raincoat from getting wet.

(D) The angle of contact $\theta$ determines the wetting behavior of a liquid on a solid surface.
If $\theta < 90^{\circ},$ the liquid wets the surface (e.g.,water on glass).
If $\theta > 90^{\circ},$ the cohesive forces between liquid molecules are stronger than the adhesive forces between the liquid and the solid surface.
Consequently,the liquid does not wet the solid surface (e.g.,mercury on glass).
Therefore,the correct condition for a liquid not to wet a solid surface is that the angle of contact is greater than $90^{\circ}.$

(A) Assertion $(A)$ is true: Water does not wet clothes containing oil or grease stains because water does not spread over the oil/grease surface. Thus,they cannot be cleaned by water alone.
Reason $(R)$ is true: The angle of contact $(\theta_c)$ between water and oil/grease is obtuse $(\theta_c > 90^{\circ})$. This indicates that water does not wet the surface,which is why detergents are needed to reduce the surface tension and change the angle of contact to make it acute,allowing the water to remove the stain.
Since the obtuse angle of contact is the physical reason why water fails to wet the oil/grease,$(R)$ is the correct explanation of $(A)$.

(C) The correct option is $C$.
Raincoats are coated with a hydrophobic material that increases the angle of contact between the water droplets and the fabric surface.
When the angle of contact is obtuse (greater than $90^{\circ}$),the liquid does not wet the surface.
This prevents the water from penetrating the fabric,thereby making the raincoat waterproof.

(A) The height of the liquid rise or fall in a capillary tube is given by $h = \frac{2T \cos \theta}{\rho gr}$.
If the contact angle $\theta = 0^{\circ}$,then $\cos 0^{\circ} = 1$,which results in a non-zero height $h = \frac{2T}{\rho gr}$. Thus,the liquid must rise in the capillary. Therefore,Statement-$I$ is false.
The contact angle $\theta$ depends on the nature of the solid surface,the liquid,and the surrounding medium (gas/vapor). Thus,it is a property of the materials involved. Therefore,Statement-$II$ is true.
Conclusion: Statement-$I$ is false and Statement-$II$ is true.

(C) The ratio is given by $K = \frac{\cos \theta_{A}}{\cos \theta_{B}}$.
For $K$ to be negative,$\cos \theta_{A}$ and $\cos \theta_{B}$ must have opposite signs.
If $\theta < 90^{\circ}$,$\cos \theta > 0$ (concave meniscus).
If $\theta > 90^{\circ}$,$\cos \theta < 0$ (convex meniscus).
Therefore,if $K < 0$,one liquid must have a concave meniscus $(\theta < 90^{\circ})$ and the other must have a convex meniscus $(\theta > 90^{\circ})$.

(A) The shape of the liquid meniscus in a capillary tube is determined by the angle of contact $\theta$ between the liquid and the solid surface.
If the angle of contact $\theta$ is acute $(\theta < 90^{\circ})$,the liquid wets the surface,and the meniscus is concave (e.g.,water in glass).
If the angle of contact $\theta$ is obtuse $(\theta > 90^{\circ})$,the liquid does not wet the surface,and the meniscus is convex (e.g.,mercury in glass).
Therefore,for the meniscus to be convex,the angle of contact must be greater than $90^{\circ}$.

(A) The correct option is $A$.
Concept: The angle of contact generally decreases with an increase in temperature.
Addition of impurities significantly affects the surface tension of a liquid,which in turn alters the angle of contact.
The angle of contact is a property that depends on the nature of the liquid and the solid surface in contact.
For a specific solid-liquid pair at a constant temperature,the angle of contact remains constant.
Therefore,statement $A$ is the only statement that is '$NOT$' true,as an increase in temperature typically decreases the angle of contact.

(A) The angle of contact $\theta$ depends on the surface tension of the liquid,the surface tension of the solid-liquid interface,and the surface tension of the solid-air interface,as given by Young's equation: $\cos \theta = \frac{T_{sa} - T_{sl}}{T_{la}}$.
When a soluble impurity is added to a liquid,it generally decreases the surface tension of the liquid $(T_{la})$.
For most liquids that wet the surface (where $\theta < 90^{\circ}$),the addition of soluble impurities (like detergents or soaps) further reduces the surface tension,which leads to a decrease in the angle of contact $\theta$.
Therefore,adding soluble impurities typically decreases the angle of contact.

(B) At the point of contact,the forces due to surface tension must be in equilibrium along the surface of the solid.
Let $S_2$ be the surface tension at the solid-air interface,$S_3$ be the surface tension at the solid-liquid interface,and $S_1$ be the surface tension at the liquid-air interface.
The force $S_1$ acts at an angle $\theta$ with the solid surface.
Resolving $S_1$ into horizontal and vertical components,the horizontal component $S_1 \cos \theta$ acts in the same direction as $S_3$.
For equilibrium along the horizontal direction of the solid surface,the forces must balance:
$S_2 = S_3 + S_1 \cos \theta$
Thus,the correct relation is $S_1 \cos \theta + S_3 = S_2$.

(D) The angle of contact is a characteristic property of the pair of materials (liquid and solid) and the surrounding medium.
It depends on the nature of the liquid and the solid surface,as well as the temperature.
It does not depend on the orientation or inclination of the solid object in the liquid.
Therefore,if the rod is placed horizontally,the angle of contact remains $120^{\circ}$.

(B) For a hydrophilic surface, the contact angle at the water-solid interface is less than $90^{\circ}$, i.e., $ < 90^{\circ}$.
This occurs because the adhesive force between the liquid molecules and the hydrophilic surface is significantly stronger than the cohesive forces within the liquid.
As a result, the liquid tends to spread over the surface, leading to a contact angle of less than $90^{\circ}$.

(D) liquid does not wet a solid surface if the angle of contact is obtuse,i.e.,greater than $90^{\circ}$.
In this condition,the cohesive forces between the liquid molecules are stronger than the adhesive forces between the liquid and the solid surface.
Consequently,the liquid tends to minimize contact with the surface,resulting in the liquid not wetting the solid.