# MHT-CET Physics Crash Course “Expression of Capillary Rise by Forces” Class 12

## “Expression of Capillary Rise by Forces” MHT-CET Class 12 Physics Crash Course | Chapter Mechanical Properties of Fluids

In this session G.S. Khairnar discussed the theory and MCQ’s of “Expression of Capillary Rise by Forces”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.

### Expression of Capillary Rise by Forces:-

Hello everyone, we have studied the concept of surface tension, angle of contact in previous articles. In this article we are going to discuss the importance of surface tension in explanation of cracking of rock, sag supply to the plant leaves, function of nib in ink pen and many more.

Capillary and capillary action is one of the most important effects of surface tension. So let’s discuss the capillary and capillary rise in detail.

Let’s discuss the concept.……………!

If the capillary tube is inserted into a liquid which wets the glass, the liquid rises in the capillary to a certain height.

Consider capillary of radius ‘r’ is dipped vertically in liquid of density ρ . Let ‘h’ is the height of liquid that rises in capillary when dipped in liquid. If ‘T’ is the surface tension of the liquid, the force acts along a tangent to the liquid meniscus, making an angle ‘θ’ with the well of the capillary. The meniscus is concave as shown in fig. below.

At point of contact the surface tension T acts tangentially to the surface, which is resolved into,

1. T cosθ- acting vertically upward.
2. T sin θ- in horizontal direction.

The horizontal component T sin θ is directed outwards due to all molecules along circumference, hence cancels each other. The only component of force acting due to surface is then Tcosθ which is nothing but the total vertical component of force is acting over complete circumference is,

∴ Total upward force on liquid = 2 π r (T cosθ)……… (1)

This force is balanced by the weight of liquid column inside capillary tube. So net downward force is given by,

∴ Total downward force on liq. = mg …….…… (2)

But Mass of liquid column, m= ρV

∴ m=ρ π r2 h

On substituting in equation (2)

∴ Total downward force on liq = ρ π r2 h g

∴ Total downward force on liquid = ρ π r2 h g   ……… (3)

For equilibrium of liquid column inside capillary

Total upward force = Total downward force

∴ 2 π r (T cosθ) = ρ π r2 h g

∴ 2 (T cosθ) = ρ r h g

Equation (4) gives the formula for the rise in liquid in capillary when it is dipped in liquid; equation (5) gives the formula for surface tension of liquid.

Some important terms…………….!

(1) Rise in capillary is inversely proportional to the radius of capillary,

(2) Rise in capillary is increases when soluble impurities are added to liquid and decreases when insoluble impurities are added in liquid.

### Let’s solve the following MCQ’s……!

Q.1) The expression for rise of liquid in capillary when dipped in liquid of surface tension T is …

Q.2) The rise of capillary when dipped in liquid if surface tension is constant is….…..

a) directly proportional to square of radius of capillary

b) directly proportional to of radius of capillary

c) inversly proportional to square of radius of capillary

d) inversly proportional to of radius of capillary

d) inversly proportional to of radius of capillary

Q.3) The rise of capillary when dipped in liquid is …..

a) directly proportional to angle of contact of for liquid

b) directly proportional to surface tension of liquid

c) inversly proportional to density of liquid

d) all of above

d) all of above

Q.4) The rise of capillary when dipped in liquid is …..

a) directly proportional to angle of contact of for liquid

b) directly proportional to surface tension of liquid

c) inversly proportional to density of liquid

d) all of above

d) all of above

Q.5) Rise of capillary when capillary of radius of 0.2 cm is dipped in soap solution of surface tension 0.065 N/m and having density of 850 kg/m3 (θ=240)

a) 31 mm

b) 3.1 mm

c) 31 cm

d) 3.1 cm

b) 3.1 mm

Q.6) Capillary of radius 0.2 cm is dipped in liquid raises level by 4 cm. The rise if liquid in capillary of radius 0.5 cm is…

a) 1.3 cm

b) 1.4 cm

c) 1.6 mm

d) 1.6 cm

d) 1.6 cm

### ♦जिल्हा नुसार जाहिराती ♦

अहमदनगर अकोला अमरावती औरंगाबाद भंडारा बुलढाणा
चंद्रपुर धुले गढ़चिरौली गोंदिया हिंगोली जलगांव
जालना कोल्हापुर लातूर मुंबई नागपुर नांदेड़
नंदुरबार नाशिक उस्मानाबाद पालघर परभानी पुणे
रायगढ़ रत्नागिरि सांगली सातारा सिंधुदुर्ग सोलापुर
ठाणे वर्धा वाशिम यवतमाल बीड

### ♦शिक्षणानुसार जाहिराती ♦

७ वी (7th) दहावी (SSC) बारावी (HSC) डिप्लोमा आय.टी.आय पदवी
पदव्युत्तर शिक्षण बी.एड एम.एड एल.एल.बी / एल.एल.एम बीएससी एमबीए
बीसीए एमसीए बी.कॉम एम.कॉम GNM/ANM एमएससी
बी.फार्म एम.फार्म बी.ई एम.ई BAMS/BHMS एम.बी.बी.एस / एम.डी
बी.टेक एम.टेक MS-CIT