Answer

Verified

409.8k+ views

**Hint:**Capillary tube is a cylindrical tube that forms a meniscus when it is dipped inside the water. The meniscus is the spherical curve that forms on the surface of the water. That meniscus has a radius. That radius of the meniscus depends upon the radius of the capillary tube. If the radius of the capillary tube is narrower, the curvature of the meniscus will be greater. If the radius of the capillary tube is wider, the curvature of the meniscus will be smaller.

**Formula used:**

\[h = \dfrac{{2T\cos \theta }}{{\rho rg}}\]

Where, \[h\]= Height of the water, \[T\]=Surface Tension of water\[(T = 0.075N/m)\], \[\theta \]= Contact angle created, \[\rho \]= Density of the water\[(1000Kg{m^{ - 3}})\], \[r\] = Radius of the capillary tube and \[g\]= Acceleration due to gravity\[(10m{s^{ - 2}})\].

**Complete step by step answer:**

Here the capillary tubes are joining together. This capillary tube is dipped vertically into the water. This is done in two ways. In the first case, the \[{T_1}\] side of the capillary tube is dipped. And in case II, \[{T_2}\] the side of the capillary tube is dipped.When the capillary tube is dipped, the level of water is raised inside the capillary tube. This rising of water causes meniscus. The height of the water rising can be found by the formula,

\[h = \dfrac{{2T\cos \theta }}{{\rho rg}}\]

When the \[{T_1}\] is dipped, the angle \[0^\circ \] is created. In this case, the height of the water can be found by the following method.

\[h = \dfrac{{2T\cos \theta }}{{\rho rg}}\]

\[ \Rightarrow h = \dfrac{{2 \times 0.075 \times \cos 0^\circ }}{{1000 \times 0.2 \times {{10}^{ - 3}} \times 10}}\]

\[h = 7.5cm\] ------------- (1)

In case II, the \[{T_2}\] side of the capillary tube is dipped, it makes \[60^\circ \] as a contact angle in the water. The height of the water is raised inside the capillary tube can be found by,

\[h = \dfrac{{2T\cos \theta }}{{\rho rg}}\]

\[ \Rightarrow h = \dfrac{{2 \times 0.075 \times \cos 60^\circ }}{{1000 \times 0.2 \times {{10}^{ - 3}} \times 10}}\]

\[\therefore h = 3.75cm\] -------------- (2)

Now let’s analyse the options. Option A can be correct. Because the height of the water inside the capillary tube is \[7.5cm\] in case I.Option B can be omitted as it recommends the height of the water inside the capillary tube is \[8.75cm\]. Therefore option B is incorrect.

Option C also can be omitted as it says that the height of the water rising depends upon the weight of the water in the meniscus. Because from the formula itself we can say that there is no place for the weight of the water in finding height. The option D is acceptable because, from equation (2), the height of the water raised in case II is \[3.75cm\]. Hence it is correct.

**Therefore the options $(A)$ and \[(D)\] are correct.**

**Note:**When the capillary tube is dipped in the water, it forms a meniscus. This meniscus is formed due to the contact angle between the water and the walls of the capillary tube. The water raised in the capillary tube depends upon the surface tension of the water, the contact angle created the density of the water, the radius of the cylindrical capillary tube, and the acceleration due to gravity.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

How do you graph the function fx 4x class 9 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

What organs are located on the left side of your body class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell