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भूमि एक अति महत्त्वपूर्ण संसाधन है। भारत का कुल क्षेत्रफल 32.8 लाख वर्ग कि०मी० है। उपलब्ध आंकड़ों के अनुसार देश की कुल भूमि के 92.7 प्रतिशत भाग का उपयोग हो रहा है। यहां भूमि का उपयोग मुख्यत: चार रूपों में होता है —

1. कृषि,
2. चरागाह,
3. वन,
4. उद्योग, यातायात, व्यापार तथा मानव आवास।

1. कृषि- भारत के कुल क्षेत्रफल के लगभग 56 प्रतिशत भाग पर कृषि की जाती है। देश में 16.3 करोड़ हेक्टेयर … भूमि शुद्ध बोये गए क्षेत्र के अधीन है। 1.3 प्रतिशत भाग फलों की कृषि के अन्तर्गत आता है। पाँच प्रतिशत क्षेत्र में परती भूमि है।

2. चरागाह- हमारे देश में चरागाहों का क्षेत्रफल बहुत ही कम है। फिर भी यहां संसार में सबसे अधिक पशु पाले जाते हैं। इन्हें प्रायः पुआल, भूसा तथा चारे की फसलों पर पाला जाता है। कुछ ऐसे क्षेत्रों में भी पशु चराये जाते हैं, जिन्हें वन क्षेत्रों के अन्तर्गत रखा गया है।

3. वन- हमारे देश में केवल 22.7 प्रतिशत से भी कम भूमि पर वन हैं। आत्मनिर्भर अर्थव्यवस्था तथा पारिस्थितिक सन्तुलन के लिए देश के एक-तिहाई क्षेत्रफल में वनों का होना आवश्यक है। अतः हमारे देश में वन-क्षेत्र वैज्ञानिक दृष्टि से बहुत कम है। भूमि उपयोग के आंकड़ों के अनुसार यहां वनों का विस्तार 6.7 करोड़ हेक्टेयर भूमि में है। परन्तु उपग्रहों द्वारा लिए गए छाया चित्रों के अनुसार यह क्षेत्र केवल 4.6 करोड़ हेक्टेयर ही है।

4. उद्योग, व्यापार, परिवहन तथा मानव आवास- देश की शेष भूमि या तो बंजर है या उसका उपयोग उद्योग, व्यापार, परिवहन तथा मानव आवास के लिए किया जा रहा है। परन्तु बढ़ती जनसंख्या तथा उच्च जीवन-स्तर के कारण मानव आवास के लिए भूमि की मांग निरन्तर बढ़ती जा रही है। परिणामस्वरूप अन्य सुविधाओं के विकास के लिए भूमि का निरन्तर अभाव होता जा रहा है।
इस प्रकार स्पष्ट है कि भारत में भूमि का उपयोग सन्तुलित नहीं है। अतः हमें भूमि के विभिन्न उपयोगों में सन्तुलन बनाए रखने के लिए प्रयत्न करना चाहिए।

कृषि के पिछड़ेपन के कारण-भारत की कृषि के पिछड़ेपन के अग्रलिखित कारण हैं —

1. कृषि की वर्षा पर निर्भरता — भारत का किसान सिंचाई के लिए अधिकतर वर्षा पर निर्भर है, परन्तु वर्षा अविश्वसनीय तथा अनिश्चित होने के कारण हमारी कृषि पिछड़ी हुई है।
2. भूमि में नाइट्रोजन का अभाव — भारत की भूमि में नाइट्रोजन की कमी है। इसका कारण यह है कि हज़ारों साल से हमारी भूमि पर कृषि हो रही है। इसके कारण हमारी भूमि की उपजाऊ शक्ति काफी कम हो गई है।
3. उचित श्रम का अभाव — हमारे कृषक दुर्बल हैं। परिणामस्वरूप वे इतना परिश्रम नहीं कर पाते जितना कि कृषि के लिए आवश्यक है।
4. खेतों का अपघटन — हमारे देश में पिता की मृत्यु के बाद भूमि उसके बेटों में बंट जाती है। इस प्रकार खेतों के आकार छोटे होते जाते हैं जिससे उत्पादन कम हो जाता है।
5. कृषि के पुराने ढंग — भारतीय किसान अभी तक पुराने ढंग से कृषि कर रहा है। इस कारण हमारी कृषि पिछड़ी
6. अच्छे बीजों का प्रयोग न करना — निर्धन होने के कारण भारतीय कृषक अच्छे बीजों का प्रयोग नहीं कर पाते। अतः हमारे खेतों में उपज कम होती है।
7. धन का अभाव — कृषि के लिए धन की बड़ी आवश्यकता होती है, परन्तु भारतीय कृषक निर्धन हैं।
8. दुर्बल पश — भारतीय किसान बैलों की सहायता से अपने खेतों में हल चलाता है। परन्तु हमारे यहां के अधिकतर बैल अच्छी नस्ल के नहीं हैं। ये बैल दुर्बल होते हैं। इनसे कृषि का पूरा कार्य नहीं लिया जा सकता।
9. निरक्षरता — भारतीय किसान निर्धन होने के अतिरिक्त निरक्षर भी हैं। अत: वह कृषि के नए ढंग अपनाने में कठिनाई अनुभव करता है।

कृषि की दशा सुधारने के उपाय-कृषि की दशा में सुधार लाने के लिए निम्नलिखित पग उठाए जा सकते हैं —

1. सहकारी कृषि- सहकारी कृषि की प्रणाली जारी करनी चाहिए। इससे खेत बड़े हो जाएंगे और सभी सुविधाएं प्राप्त हो जाएंगी।
2. सिंचाई की अधिक सुविधाएं- कृषि की स्थिति में सुधार लाने के लिए सिंचाई की सुविधाएं बढ़ाई जानी चाहिएं।
3. गहन खेती- हमारे देश में किसान को गहन कृषि के ढंगों को अपनाना चाहिए। इससे भूमि की शक्ति बढ़ जाती है और थोड़ी-सी भूमि से भी अधिक ऊपज प्राप्त होती है।
4. अच्छे बीज और खाद- सरकार को चाहिए कि वह किसानों को सस्ते दामों पर अच्छे बीज दे। अच्छी खाद खरीदने के लिए उन्हें सरकार द्वारा सहायता मिलनी चाहिए।
5. नवीन कृषि यत्रों का प्रयोग - यदि कृषि के नवीन यन्त्रों का प्रयोग किया जाए तो कृषि में काफी सुधार हो सकता है। सरकार को इन औजारों को खरीदने के लिए कृषक की धन से सहायता करनी चाहिए।

जानकारी को सतत आवृत्ति में दर्शाने के लिए आलेख का उपयोग किया जाता है ।

असतत जानकारी दर्शाने के लिए आकृति का उपयोग किया जाता है ।

सही विकल्प है (A) प्रतिशत स्वरूप

आकृति स्वरूप जानकारी से सामान्य प्रजा में सरलता से समझ खड़ी करके अपने अध्ययन को रुचिपूर्वक समझा सकते हैं ।

अध्ययन करने से कम्प्यूटर का उपयोग निम्नानुसार है :

1. प्रेजन्टेशन बनाने और तैयार करने के लिए कम्प्यूटर का उपयोग किया जा सकता है ।
2. एक्सल वर्कशीट के द्वारा बड़े पैमाने पर सांख्यकीय जानकारी को प्रस्तुत कर सकते हैं ।
3. आलेख और आकृति बनाने के लिए कम्प्यूटर अधिक उपयोगी है ।
4. जानकारी के संग्रह के लिए कम्प्यूटर उपयोगी है ।
5. सांख्यिकी के एडवान्स प्रोग्रामों के लिए गणना करता है ।

प्रति हेक्टेयर गेहूं उत्पादन तथा केन्द्रीय भण्डार को गेहूं देने में पंजाब का देश में प्रथम स्थान है।

20% को वृत्त में दर्शाने के लिए (20 × 360): 100 = 72°) 72° का कोण बनेगा ।

वृत्त का कुल क्षेत्रफल 360° होता है ।

सही विकल्प है (D) 360°

Divino’s earning for 10 days = ₹ 1500

His earning in 1 day = 1500/10 = ₹ 150

Divino’s earning in 30 days = 150 × 30 = ₹ 4,500

Divino earns ₹ 4,500 in 30 days.

(a) Bachhu Manjhi earns in one year is Rs.36000.

(b) Bachhu manjhi earns Rs.42000 in 14 months.

C) both A and B

Correct option (B) Bifocal lens whose upper portion is concave lens and lower portion is convex lens   

Explanation:

The upper portion (concave lens) facilitates distant vision and the lower portion (convex lens) facilitates near vision.

(i) Presbyopia.

(ii) He shall have to use both kinds of lenses. Convex lens for long sightedness and a concave lens for short-sightedness.

The ability of eye lens to adjust its focal length to form the sharp image of the object at varying distances on the retina is called its power of accommodation. When we see the nearby object, the ciliary muscles contract, it increases the thickness of eye lens. The eye lens then becomes thicker. As a result, the focal length of eye lens decreases in such a way that the clear sharp image of nearby object is formed on the retina. Thus, the object is seen clearly to us.

When we see the distant object, these muscles becomes relaxed, thus the eye lens becomes thinner, and consequently focal length of the lens increases. Therefore, the parallel rays coming from the distant object are focused on the retina and object is seen clearly to us. Thus, the accommodation power of an eye helps a person to see nearby as well as distant objects clearly. 

• Our eyes can focus on the images from varied distance by changing its focal length of lens. 
• Action of Ciliary muscle helps changing focal length of the lens

Acceleration.

(d) In the side mirror, the speed of the approaching car would appear to increase as the distance between the cars decreases.

The instant of time which is taken after the origin of time (i.e., zero-time) is called positive time instant of time which is taken before the origin of time is called the negative time.

When the speed of the body is decreasing.

(i) Since, position is increasing with time so it is a case of positive acceleration.

(ii) The upward curve of the given graph indicates positive acceleration.

(iii) The dropping of curve i.e. downward curve indicates negative acceleration.

(iv) OABCD represents positive acceleration, DE represents zero acceleration.

As, a = 3t² + 2t + 2 ⇒ \(\frac{dv}{dt}\) = 3t² + 2t + 2

Integrating

∫ dv = ∫ (3t² + 2t + 2)dt

v = t³ + t² + 2t + c

at, t = 0, v = 0

∴ c = 2

now at t=2, v= 8 + 4 + 4 + 2 = 18 m/s

Here, x = 8t² - 3t³

(i) when t = 0, x = 0

when t = 2s, x =8(2)² - 3(2)³ = 32 - 24 = 8 m.

Displacement in time interval (2 -0 = 2s) = 8m - 0 = 8 m.

Average velocity = Displacement /Time interval = 8m/2s = 4 ms^-1.

(ii) When, t = 0, x = 0

when t = 3s, x = 8(3)² -3(3)³ = 72 - 81 = -9m

Net displacement = -9 - 0 = -9 m

Time interval = 3 - 0 = 3s.

Average velocity = -9m/3s = -3ms^-1.

Data : y = 0.1 sin 4π (50t – 0.1 x) 

= 0.1 sin 2π (100t – 0.2 x)

= 0.1 sin 2π( 100t –\(\frac x5\))

Let us compare this equation with that of a simple harmonic progressive wave.

∴ y = A sin 2π(nt – \(\frac x5\)) = 0.1 sin2π(100t – \(\frac x5\))

Comparing the quantities on both sides, we get,

1. amplitude (A) = 0.1 m 

2. frequency (n) = 100 Hz 

3. wavelength (λ) = 5 m 

4. speed (v) = nλ = 100 × 5 = 500 m/s

Data : A = 0.05 m, T = 0.04 s, v = 12.5 m/s 

∴ Equation of the wave travelling in the positive direction of the x-axis is

y = A sin \(\frac{2\pi}T\)\((t-\frac{x}v)\)

= 0.05 sin \(\frac{2\pi}{0.04}\)\((t-\frac{x}{12.5})\) meter

OR

v = \(\frac{\lambda}T\)

\(\therefore\) \(\lambda\) = vT = 12.5 x 0.04 = 0.5 m

\(\therefore\) The equation of the wave travelling in the positive direction of the x-axis is

y = A sin \({2\pi}\)\((\frac tT-\frac x\lambda)\)

= 0.05 sin \({2\pi}\)\((\frac t{0.04}-\frac x{0.5})\) meter

Here m = 10 kg, h = 0.5 m, n = 1000

(a) Work done against the gravitational force,

W = n mgh

= 1000 x (10 x 9.8 x 0.5) = 49000 J

(b) Mechanical energy supplied by 1 kg of fat

= 3 x 10⁷ J x 20/100

= 0.76 x 10⁷ J/kg

Fat used up by the dieter = {1}/{0.76 x 10⁷} x 49000

= 6.45 x 10^-3 kg

Students can solve these MCQ Questions for Class 8 with Answers and assess their preparation level. Students are well-considered to practice the MCQ Questions for Class 8 Science with Answers is available here. MCQ Questions for Class 8 Science with Answers are prepared as per the Latest Exam Pattern. These MCQ Questions of Force and Pressure with answers pave for a quick revision of the Chapter by helping you to enhance subject knowledge.

CBSE Class 8 Science MCQ Questions of Force and Pressure are prepared by subject experts to help students know the important topics and fundamental concepts. Students should practice objective types of questions to score well in the exam. All the questions are provided with correct answers. All the questions are provided with correct answers.

Practice Class 8 Science MCQ Questions chapter-wise

1. The pressure which is exerted by the air around us is known as

(a) force
(b) atmospheric pressure
(c) muscular force
(d) friction

2. Force acting on per unit area is called

(a) non-contact forces
(b) contact forces
(c) force
(d) pressure

3. A ___________ exerted by an object on another is a force.

(a) Push or pull
(b) Contact or non-contact force
(c) Pressure
(d) Magnitude

4. The force exerted by the earth to pull the object towards itself is called

(a) electrostatic force
(b) gravitational force
(c) muscular force
(d) contact force

5. Muscular force is also called ___________ force.

(a) non-contact
(b) contact
(c) gravitational
(d) magnetic

6. The force exerted by a charged body on another char

(a) gravitational force
(b) electrostatic force
(c) non-contact force
(d) contact force

7. The force exerted by our muscles is called

(a) electrostatic force
(b) muscular force
(c) gravitational force
(d) non-contact force

8. A spring balance is used for measuring

(a) mass
(b) weight
(c) pressure
(d) speed

9. When two forces act in opposite directions, then net force acting is the

(a) sum of two forces
(b) difference between two forces
(c) both of these
(d) none of these

10. The strength of force is expressed by its

(a) weight
(b) mass
(c) magnitude
(d) longitudinal force

11. State of motion is described by

(a) Position of rest
(b) Position of motion
(c) Both by the state of rest or motion
(d) None of these

12. During dry weather, while combing hair, sometimes we experience hair flying apart. The force respon¬sible for this is

(a) force of gravity
(b) force of friction
(c) electrostatic force
(d) magnetic force

13. Two objects repel each other. This repulsion could be due to

(a) frictional force only
(b) electrostatic force only
(c) magnetic force only
(d) either a magnetic or an electrostatic force

14. Which one of the following forces is a contact force?

(a) Force of gravity
(b) Magnetic force
(c) Force of friction
(d) Electrostatic force

15. A ball rolling on the ground slows down and finally stops. This is because of

(a) Force
(b) Less force applied
(c) Friction
(d) None of the above

16. Frictional force always acts in which direction?

(a) On any direction
(b) Along the direction of motion
(c) Perpendicular to the direction of motion
(d) Opposite to the direction of motion

17. Which of these is an example of a non-contact force?

(a) A toy car slides down the ramp
(b) A bar magnet moves a paperclip without touching it
(c) A child lifts a book lying on the table
(d) A marble rolling on the carpet slows down

18. Gravity is

(a) Repulsive
(b) Attraction + Repulsive force
(c) Attractive force
(d) Not a force

19. A batsman hits the ball for a boundary past the bowler i.e. four runs. The batsman thus

(a) Changes the direction & speed of the ball
(b) Does not change the direction but speed only
(c) Does not change the speed but direction only
(d) Does not change either direction or speed

20. When a given force is applied on larger area of contact the pressure exerted by it:

(a) increases
(b) decreases
(c) does not change
(d) none of these

21. The pressure exerted by a liquid:

(a) decreases with depth
(b) does not change with depth
(c) increases with depth
(d) is different in different directions at the same depth

22. We are not crushed under the weight of air because:

(a) air has no weight
(b) the pressure inside our bodies is equal to atmospheric pressure
(c) the pressure inside our bodies is more than atmospheric pressure
(d) none of these

23. Two objects repel each other. This repulsion could be due to

(a) frictional force only
(b) electrostatic force only
(c) magnetic force only
(d) either a magnetic or an electrostatic force

24. Which one is an example that shows that force can change shape and size of object?

(a) Force applied to increase the speed
(b) Force applied on cricket ball
(c) Force applied on large stone
(d) Force applied on inflated balloon

25. The tendency of a body to maintain its state of rest or uniform motion is called

(a) Gravity
(b) Inertia
(c) Weight
(d) Acceleration

Answer:

1. Answer: (b) atmospheric pressure

Explanation: That pressure is called atmospheric pressure, or air pressure. It is the force exerted on a surface by the air above it as gravity pulls it to Earth. Atmospheric pressure is commonly measured with a barometer.

2. Answer: (d) pressure

Explanation: Pressure is defined as force per unit area. The standard unit for pressure is the Pascal, which is a Newton per square meter. P = F/A

3. Answer: (a) Push or pull

Explanation: Force is a push or a pull in a particular direction that changes the orientation of the object.

4. Answer: (b) gravitational force

Explanation: The attraction force exerted by the earth on any object is called or is termed gravity.

5. Answer: (b) Contact

Explanation:  Muscular force is a contact force. The electrostatic force is a non-contact force. Contact Force is a force that can be applied only when it is in contact with an object is called a contact force.

6. Answer: (b) electrostatic force

Explanation: The force exerted by an electrostatic charge or an electrically charged object is known as electrostatic force. An electrically charged object can exert an electrostatic force on another body, be it a charged body or an uncharged body.

7. Answer: (b) muscular force

Explanation: The force caused by the action of muscles in our body is known as muscular force.

8. Answer: (b) weight

Explanation: Spring balance is used to determine the force acting on the object (weight). Spring balance works on the principle of Hooke's law.

9. Answer: (b) difference between two forces

Explanation: Forces applied on an object in the same direction add to one another.If two forces act in the opposite directions on an object, the net force acting on it is the difference between the two forces.

10. Answer: (c) magnitude

Explanation: The strength of a force is expressed by its magnitude. The magnitude of a force is expressed in the SI unit of force called Newton.

11. Answer: (c) Both by the state of rest or motion

Explanation: The state of motion is described by both the state of rest and motion. There are two types of motion that are uniform and non-uniform motion. When the speed of the object is zero it is said to be at rest but still in the state of motion

12. Answer: (c) electrostatic force

Explanation: When two objects are rubbed together, there is an exchange of electrons. During dry weather, the hair follicles are straightened up and they have picked up electrons during the rubbing process. The follicles have the like charges that repel each other.The force responsible for this is the electrostatic force.

13.Answer: (d) either a magnetic or an electrostatic force

Explanation: Frictional force is applied along the surfaces and depends on contact. hence it is not a repulsive force. Electrostatic and magnetic forces can be either attractive or repulsive. Here, when two objects are experiencing repulsive force because there may be an electrostatic force or a magnetic force.

14. Answer: (c) Force of friction

Explanation: Friction is a surface phenomenon. When two surfaces have irregularities that come in contact they get interlocked preventing them from sliding against each other. So, the frictional force is a contact force dependent on the surface.

15. Answer: (c) Friction

Explanation: When a ball is rolling on ground their is a friction force which retards the motion of ball and make it zero finally.

16. Answer: (d) Opposite to the direction of motion

Explanation: Frictional force offers the resistance to the applied force opposing its motion. Thus, it always acts in the direction opposite to that of the object in motion. If force is applied to the left, then friction acts in the right.

17. Answer: (b) A bar magnet moves a paperclip without touching it

Explanation:  A bar magnet moving a paper clip exerts magnetic force of repulsion or attraction and we know that magnetic force is a non contact force in nature.

18. Answer: (c) Attractive force

Explanation: Gravitational force -an attractive force that exists between all objects with mass; an object with mass attracts another object with mass; the magnitude of the force is directly proportional to the masses of the two objects and inversely proportional to the square of the distance between the two objects.

19. Answer: (a) Changes the direction & speed of the ball

Explanation: The correct answer is changes the direction and speed of the ball. A batsman hits the ball for a boundary past the bowler i.e. four runs. The batsman thus changes the direction and speed of the ball. Force can change the state of motion of an object.

20. Answer: (b) decreases

Explanation:  When a given force is applied on larger area of contact than the pressure exerted by it decreases.

21. Answer: (c) increases with depth

Explanation:  The pressure exerted by a liquid increases with depth.

22. Answer: (b) the pressure inside our bodies is equal to atmospheric pressure

Explanation:  The pressure inside our bodies is equal to the atmospheric pressure and cancels the pressure from outside.

23. Answer: (d) either a magnetic or an electrostatic force

Explanation: when two objects are experiencing repulsive force because there may be an electrostatic force or a magnetic force.

24. Answer: (d) Force applied on inflated balloon

Explanation: Force applied on inflated balloon is an example that shows that force can change shape and size of object. Force applied on inflated balloon is an example that shows that force can change shape and size of object.

25. Answer: (b) Inertia

Explanation: Inertia is the tendency of an object to resist changes in its state of motion.  The state of motion of an object is defined by its velocity - the speed with a direction.

Click here Practice MCQ Question for Force and Pressure Class 8

The snow shoes have large, flat soles so they exert less pressure (= force /area) on the soft snow and stop the wearer from sinking into it.

The maximum value of static friction upto which body does not move is called limiting friction. 

(i) The magnitude of limiting friction between any two bodies in contact is directly proportional to the normal reaction between them.

F₁ ∝ R or F₁ = µ_s R

(ii) Direction of the force of limiting friction is always opposite to the direction in which one body is at the verge of moving.

(iii) Coefficient of static friction : 

(a) µ_s is called coefficient of static friction. 

(b) Dimension : [M⁰L⁰T⁰] 

(c) Unit : It has no unit. 

(d) Value of µ_s lies in between 0 and 1 

(e) Value of µ depends on material and nature of surfaces in contact. 

(f) Value of µ does not depend upon apparent area of contact.

The physical quantities which have both magnitude and direction are called vectors. 

e.g. displacement, velocity, acceleration, force, momentum, etc. 

Data : L = 36 cm = 0.36 m, n = 280 Hz, T = 24.5 N

n = \(\frac 1{2L}\)\(\sqrt{\frac Tm}\)

∴ Linear density, m = \(\frac T{4L^2n^2}\)

∴ m = \(\frac{24.5}{4(0.36)^2(280)^2}\)

= 6.0 × 10^-4 kg/m

The process of splitting a vector into two or more vectors is known as resolution of the vector. The vectors into which the given vector is split are called component vectors. A vector A can be resolved into components along two given vectors a and b lying in the same plane in one and only one way. 

When a vector A is multiplied by a real number λ, we get another vector λ A. The magnitude of λ A is λ times the magnitude of A. If λ is positive, then the direction of λ A is same as that of A. If λ is negative, then the direction of λ A is opposite to that of A.

(i) Unit vector: A unit vector is a vector of unit magnitude drawn in the direction of a given vector.

(ii) Free vector: A vector whose initial point is not fixed is called a free vector or non-localised vector.

(iii) Co-initial vector: The vectors which have the same initial point are called co-initial vectors.

(iv) Co-terminus vectors: The vectors which have the common terminal point are called co-terminus vectors.

Vector or cross product for two vectors A and B inclined at an angle θ, the vector or cross product is defined as A x B = A B sinθ , where , is a unit vector perpendicular to the plane of A and B. 

Geometrical interpretation of vector product: The magnitude of the vector product of two vectors is equal to 

(i) the area of the parallelogram formed by the two vectors as its adjacent sides and 

(ii) twice the area of the triangle formed by the two vectors as its adjacent sides.

Correct option is (D) λ

Pipe closed at one end : fundamental frequency,

n_c = \(\frac v{4L_c}\)

column is 51.8 cm.

n_o = \(\frac v{2L_o}\)

In this case, the frequency of the third over tone = \(\frac {4v}{2L_o}\) = \(\frac {2v}{L_o}\)

By the data, \(\frac v{4L_c}\) = \(\frac {2v}{L_o}\)

∴ \(\frac {L_o}{L_c}\) = 8 or \(\frac {L_c}{L_o}\) = \(\frac18\)

Let L be the length of the pipe open at both ends whose fundamental frequency is n. Then, ignoring the end correction, n = \(\frac v{2L}\) where v is the speed of sound in air.

When the pipe is immersed vertically in water up to half its length, it becomes a pipe closed at one end with an air column of length L’ = L / 2. Then, its fundamental frequency n’ is

n' = \(\frac v{4L'}\) = \(\frac v{4(L/2)}\) = \(\frac v{2L}\)

which is equal to n, the fundamental frequency of the open pipe.

Let L_O and L_C be the lengths of a pipe open at both ends and a pipe closed at one end, respectively. Let n_O and n_C be their corresponding fundamental frequencies. Then, ignoring the end corrections,

n_O = \(\frac v{2L_O}\) and n_C = \(\frac v{4L_O}\)

where v is the speed of the sound in air.

Given that L_C = L and L_O = 2L,

n_O = \(\frac v{4L}\)and n_C = \(\frac v{4L}\)

∴ n_O = n_C

Let L_O and L_C be the lengths of a pipe open at both ends and a pipe closed at one end, respectively. Let n_O and n_C be their corresponding fundamental frequencies. Then, ignoring the end corrections,

n_O = \(\frac v{2L_O}\) and n_C = \(\frac v{4L_C}\)

where v is the speed of the sound in air.

Given that L_O = L_C = L (say),

n_O = \(\frac v{2L}\) and n_O = \(\frac v{4L}\)

∴ n_O = 2 \((\frac v{4L})\) = 2n_C

Open pipe. 

1. Second harmonic = 2 × 200 = 400 Hz 

2. Third overtone = fourth harmonic = 4 × 200 = 800 Hz.

A stationary wave is set up in a bounded medium in which the boundary could be a rigid support (i.e., a fixed end, as for instance a string stretched between two rigid supports) or a free end (as for instance an air column in a cylindrical tube with one or both ends open). The boundary conditions limit the possible stationary waves and only a discrete set of frequencies is allowed.

The lowest allowed frequency, n , is called the fundamental frequency of vibration. Integral multiples of the fundamental frequency are called the harmonics, the fundamental frequency being the fundamental or 2n , the third harmonic is 3n , and so on.

The higher allowed frequencies are called the overtones. Above the fundamental, the first allowed frequency is called the first overtone, the next higher frequency is the second overtone, and ‘so on. The relation between overtones and allowed harmonics depends on the system under consideration.

Bulk modulus, K = \(\frac{\frac{p}{ΔV}}{V}\) = \(\frac{pV}{ΔV}\)

As perfect rigid body does not change it’s shape even after infinite force. Hence ∆V = 0

Or k = \(\frac{PV}{0}\) = ∞

Therefore, Bulk modulus for a perfect rigid body is infinity.

The Bulk modulus for a perfect rigid body - Infinite

P/Q = R/S 

⇒ 4/8 = 2/x

⇒ x = 4 Ω

माना, घड़ी की छोटी सुई की लम्बाई (त्रिज्या) r₁ = 4 सेमी

तथा घड़ी की बड़ी सुई की लम्बाई (त्रिज्या) r₂ = 6 सेमी

∵ घड़ी की छोटी सुई 12 घण्टे में एक चक्कर लगाती है।

∴ 2 दिन (48 घण्टे) में 4 चक्कर लगायेंगी

अतः घड़ी की छोटी सुई द्वारा 2 दिन में चली गयी दूरी = 2π₁ × 4

= 2 x 22/7 x 4 x 4 = 704/4 सेमी

तथा घड़ी की बड़ी सुई 1 घण्टे में एक चक्कर लगाती है तब वह 2 दिन (48 घण्टे) में 48 चक्कर लगायेंगी।

अतः घड़ी की बड़ी सुई द्वारा 2 दिन में चली गई दूरी = 2πr₂ × 48

= 2 x 22/7 x 6 x 48 = 12672/7 सेमी

दोनों सुईयों द्वारा 2 दिनों में चली गई दूरियों का योग

704/4 + 12672/7 = 13376/7 = 1910.85 सेमी

वृत्त की त्रिज्या r = 5.2 सेमी तथा त्रिज्यखण्ड की परिधि = 16.4 सेमी

l + 2r = 16.4

l + 2 × 5.2 = 16.4

l + 10.4 = 16.4

l = 16.4 – 10.4 = 6 सेमी

त्रिज्यखण्ड का क्षेत्रफल = 1/2 l r = 1/2 x 6 x 5.2 = 15.6 सेमी²

वृत्ताकार प्लॉट का व्यास = 40 मीटर

वृत्ताकार प्लॉट की त्रिज्या r = 40/2 = 20 मीटर

रास्ते की चौड़ाई = 3.5 मीटर

रास्ते सहित वृत्ताकार प्लॉट की त्रिज्या R = 20 + 3.5 = 23.5 मीटर

तब रास्ते का क्षेत्रफल = π [R² – r²]

= 22/7(23.5)² – (20)²]

= 22/7[552.25 – 400]

= 22/7 x 152.25 = 22 x 21.75

= 478.5 सेमी²

रास्ते पर ₹ 4 प्रति वर्ग मीटर की दर से घास लगाने का खर्च = 478.5 × 4 = ₹1914