1.1हमें मात्रकों की आवश्यकता क्यों है?

कल्पना कीजिए कि आप किसी से कहते हैं, “मेज 5 लंबी है।” पाँच क्या? पाँच इंच? पाँच फीट? या पाँच मीटर? बिना किसी मात्रक के, संख्या “5” का कोई अर्थ नहीं रह जाता। एक मात्रक (Unit) सर्वसम्मत अंतरराष्ट्रीय मानक होता है, जिसके साथ हम भौतिक राशियों की तुलना करते हैं, ताकि हर व्यक्ति एक ही माप को एक ही अर्थ में समझ सके।

भौतिकी में केवल कुछ ही मूल राशियां (Fundamental/Base Quantities) होती हैं — जैसे लंबाई, द्रव्यमान और समय — जिन्हें और छोटे घटकों में नहीं तोड़ा जा सकता। शेष सभी भौतिक राशियां (जैसे चाल, बल, ऊर्जा, दाब) इन्हीं मूल राशियों के संयोजन से बनती हैं। संयुक्त राशियों के मात्रकों को व्युत्पन्न मात्रक (Derived Units) कहा जाता है।

1.2मात्रकों की अंतर्राष्ट्रीय प्रणाली (SI)

प्राचीन समय में, अलग-अलग देश अलग-अलग प्रणालियों का उपयोग करते थे — जैसे CGS (सेन्टीमीटर-ग्राम-सेकंड), FPS (फुट-पाउंड-सेकंड, ब्रिटेन व अमरीका में प्रचलित), तथा MKS (मीटर-किलोग्राम-सेकंड)। इससे विभिन्न देशों के वैज्ञानिकों के बीच शोध साझा करते समय भ्रम पैदा होता था।

इसलिए, संपूर्ण विश्व ने एक सर्वमान्य प्रणाली अपनाई: SI प्रणाली (Système International d’Unités — फ्रांसीसी भाषा में “मात्रकों की अंतर्राष्ट्रीय प्रणाली”)। यह 7 मूल मात्रकों पर आधारित है, जिनमें से प्रत्येक को एक स्थिर नियतांक (Physical Constant) से परिभाषित किया गया है ताकि दुनिया में कहीं भी कोई भी वैज्ञानिक इन्हें पूरी शुद्धता से पुनरुत्पादित कर सके।

7 मूल मात्रक (Base Units)

इन 7 मूल मात्रकों के अतिरिक्त कोण मापने के लिए दो पूरक मात्रक भी हैं: समतल कोण के लिए रेडियन (radian – rad) और घन कोण के लिए स्टेरेडियन (steradian – sr)। ये दोनों “विमाहीन” (Dimensionless) राशियां हैं — अर्थात ये केवल दो समान राशियों के अनुपात हैं (जैसे चाप की लंबाई / त्रिज्या), इसलिए इनकी कोई भौतिक विमा नहीं होती।

1.3सार्थक अंक (Significant Figures)

प्रत्येक मापन में कुछ न कुछ अनिश्चितता होती है — कोई भी मापक यंत्र शत-प्रतिशत परिशुद्ध नहीं होता। सार्थक अंक हमें यह बताते हैं कि किसी मान को कितनी यथार्थता के साथ मापा गया है, ताकि हम उपकरण की क्षमता से अधिक यथार्थता का दावा न करें।

सार्थक अंक गिनने के सरल नियम

• सभी गैर-शून्य (Non-zero) अंक सार्थक होते हैं। 247 में 3 सार्थक अंक हैं।
• दो गैर-शून्य अंकों के बीच आने वाले सभी शून्य सार्थक होते हैं। 1005 में 4 सार्थक अंक हैं।
• प्रथम गैर-शून्य अंक से पहले आने वाले प्रारंभिक शून्य सार्थक नहीं होते। 0.0025 में केवल 2 सार्थक अंक हैं (2 और 5)।
• दशमलव बिंदु के बिना अंत में आने वाले शून्य सार्थक नहीं होते। 1200 में केवल 2 सार्थक अंक हैं (जब तक कि इसे वैज्ञानिक संकेतन में न लिखा जाए)।
• दशमलव बिंदु के बाद अंत में आने वाले शून्य हमेशा सार्थक होते हैं। 3.500 में 4 सार्थक अंक हैं — क्योंकि इन शून्यों को जानबूझकर मापा और दर्ज किया गया है।

गणितीय गणनाओं के नियम

गुणा/भाग: अंतिम उत्तर में केवल उतने ही सार्थक अंक होने चाहिए जितने कि सबसे कम सार्थक अंक वाली दी गई राशि में हैं।

योग/घटाव: अंतिम उत्तर में दशमलव के बाद केवल उतने ही स्थान होने चाहिए जितने कि सबसे कम दशमलव स्थान वाली दी गई राशि में हैं।

1.4भौतिक राशियों की विमाएं (Dimensions)

किसी भी भौतिक राशि को मूल राशियों के संयोजन के रूप में व्यक्त किया जा सकता है — मुख्य रूप से द्रव्यमान [M], लंबाई [L], और समय [T] (तथा आवश्यकतानुसार धारा, ताप आदि)। इस संयोजन को उस राशि की विमा (Dimension) कहते हैं।

उदाहरण के लिए, चाल “प्रति इकाई समय में तय की गई दूरी” है, इसलिए इसकी विमा लंबाई को समय से भाग देने पर प्राप्त होती है:

बल = द्रव्यमान × त्वरण = द्रव्यमान × (लंबाई / समय²), इसलिए:

1.5विमीय सूत्र एवं विमीय समीकरण

जब हम किसी भौतिक राशि को उसकी विमाओं के पदों में व्यक्त करते हैं, तो इसे विमीय सूत्र (Dimensional Formula) कहते हैं। जब इसे समीकरण के रूप में लिखा जाता है, तो यह विमीय समीकरण (Dimensional Equation) कहलाता है।

1.6विमीय विश्लेषण और इसके उपयोग

विमीय विश्लेषण का मुख्य आधार विमाओं की समांगता का सिद्धांत (Principle of Homogeneity of Dimensions) है: “हम केवल उन्हीं भौतिक राशियों को जोड़ या घटा सकते हैं जिनकी विमाएं समान हों।” आप “5 किग्रा” में “3 मीटर” नहीं जोड़ सकते — यह भौतिक रूप से निरर्थक है।

उपयोग 1: समीकरण की सत्यता की जांच करना

उपयोग 2: विभिन्न भौतिक राशियों के बीच संबंध (सूत्र) स्थापित करना

यदि हमें यह अनुमान हो कि कोई भौतिक राशि किन-किन अन्य राशियों पर निर्भर करती है, तो विमीय विश्लेषण के उपयोग से हम उनके बीच का सूत्र व्युत्पन्न कर सकते हैं — हालांकि यह सूत्र में आने वाले आंकिक नियतांक (Numerical Constant) का मान नहीं बता सकता।

विमीय विश्लेषण की सीमाएं (Limitations)

• यह सूत्र में आने वाले बीजीय नियतांकों (जैसे 2, ½, या π) का मान ज्ञात नहीं कर सकता।
• यह उन विभिन्न राशियों के बीच भेद नहीं कर सकता जिनकी विमाएं समान होती हैं (उदाहरण के लिए: कार्य और बल-आघूर्ण दोनों का विमीय सूत्र समान है, परंतु वे भौतिक रूप से भिन्न हैं)।
• यह केवल तभी कार्य करता है जब आपको पहले से ज्ञात हो कि कौन-कौन सी राशियां प्रक्रिया में शामिल हैं।
• त्रिकोणमितीय, चरघातांकी (exponential) और लघुगणकीय (logarithmic) पदों वाले सूत्रों का निगमन इससे नहीं किया जा सकता।

1. The Concept of Force

A force can: (i) make an object move from rest, (ii) change the speed or direction of a moving object, and (iii) change the shape of an object (e.g., kicking a ball, striking a ball with a bat, squeezing a lemon).

1.1 Measuring the Magnitude of a Force

A spring balance measures the force with which you pull on the spring inside it — it can measure weight (gravitational force) or force in general.

2. Balanced and Unbalanced Forces

Usually, more than one force acts on an object simultaneously (e.g., pushing a box: applied force + friction; a floating ball: gravity + buoyant force).

2.1 Calculating Net Force

3. The Force of Friction

Friction is the force that opposes relative motion (or attempted motion) between two surfaces in contact. It always acts opposite to the direction of motion.

3.1 Activities 6.1 & 6.2 — Friction Depends on Surface Nature

4. Newton’s First Law of Motion (Law of Inertia)

If net force = 0 → acceleration = 0 → object cannot begin to move or change its velocity.

5. Newton’s Second Law of Motion

A force produces acceleration. Experiments (pulling a cart with varying weights via a pulley system) show:

• For a fixed mass, acceleration increases as net force increases (larger force → larger acceleration)
• For a fixed force, acceleration decreases as mass increases (larger mass → smaller acceleration)

5.1 Newton’s Second Law in Everyday Life

• Catching a fast ball: pulling hands back while catching increases the time over which velocity drops to zero → reduces acceleration → reduces force on hands (less injury)
• Airbags: increase the time of impact during a collision → reduce deceleration → reduce force on the passenger
• Cracking a coconut: very short stopping time on hitting the ground → very large force → shell breaks

Solved Numericals — Newton’s Second Law

6. Newton’s Third Law of Motion

6.1 Everyday Applications

• Walking/running: feet push the ground backward; the ground pushes feet forward (via friction) — here friction helps motion rather than opposing it
• Climbing a tree: legs push the trunk down; friction pushes the person up — harder on smooth (low-friction) trunks
• Rocket launch: engine expels gas downward; gas exerts equal-opposite force on rocket upward; when this exceeds the rocket’s weight, it lifts off
• Chandrayaan-3’s Vikram lander: fired its engine in the direction of motion (forward) to produce a backward reaction force, slowing it down for a soft lunar landing

6.2 Newton’s Third Law Applies to All Force Types

Not just contact forces — also applies to non-contact forces: two magnets repel/attract each other equally; two charged balloons apply equal electrostatic forces; the Earth and a fruit apply equal gravitational forces on each other.

7. Forces on a System of Objects

For two objects connected by a string (e.g., two boxes, masses $m_1$ and $m_2$, pulled by external force $F$), treat them as a single system: internal forces (tension $T$) cancel out within the system; only the external force $F$ matters.

8. Quick Summary Table — All Three Laws

9. Exam Question Bank

A. MCQ / Assertion–Reason (1 mark each)

B. Short Answer (2–3 marks)

C. Numerical Problems

D. Long Answer / HOTS (4–5 marks)

1. The Ancient Origins of Atomic Theory

Over 2,000 years ago, thinkers in both ancient India and ancient Greece independently asked: What is everything made up of?

Following Dalton, scientists sought answers to: What are atoms made of? What would they look like? What makes atoms of one element different from another?

2. Evolution of Atomic Models

Discovery of radioactivity (certain elements emitting invisible energy/particles called radiation) in the late 19th century proved that atoms are not indivisible — they must contain smaller particles.

2.1 Thomson’s Model (1897) — “Plum Pudding”

Since atoms are neutral overall, Thomson had to explain where the positive charge sits. He proposed the atom as a sphere of positive charge with electrons embedded in it — like a pudding studded with plums, or seeds in a watermelon.

2.2 Testing Thomson’s Model — The Gold Foil Experiment (1911)

2.3 Rutherford’s Nuclear (Planetary) Model

Based on the gold foil results, Rutherford proposed:

• Most of an atom is empty space
• All positive charge and most mass is concentrated in a tiny, dense central region — the nucleus
• Electrons revolve around the nucleus like planets around the Sun — the planetary model

Discovery of the Proton

Rutherford showed the nucleus carries positive charge from particles called protons — much heavier than electrons, with charge equal and opposite to an electron’s. For a neutral atom: number of protons = number of electrons.

2.4 Bohr’s Model (1913) — Fixed Energy Levels

Niels Bohr proposed that electrons:

• Move only in fixed circular paths called stationary states, orbits, or shells — not randomly
• Each shell has a definite energy — hence called energy levels, labelled K, L, M, N… (or $n = 1, 2, 3, 4…$)
• Do not lose energy while moving in a fixed shell (this is the key postulate that fixes Rutherford’s stability problem)
• K-shell ($n=1$, closest to nucleus) has the least energy; energy increases with distance from the nucleus
• An electron changes shells only by absorbing or releasing energy exactly equal to the difference between the two shells’ energies
• Each shell holds only a limited number of electrons

3. Discovery of the Neutron & the Three Subatomic Particles

A puzzle remained: a helium atom (2 protons) has about 4× the mass of a hydrogen atom (1 proton) — not 2×. This suggested another mass-contributing particle existed.

4. Symbols of Elements

Dalton (1803) introduced pictorial symbols. Berzelius (1813) proposed deriving symbols from Latin names — giving us modern alphabetic symbols. Today, IUPAC approves all element names/symbols internationally.

Rules for Writing Symbols

• Often the first letter, or first two letters, of the element’s name
• First letter always capital; second letter (if any) always lowercase — e.g., Aluminium = Al (not AL), Cobalt = Co (not CO)
• Some symbols use a letter other than the second letter — e.g., Chlorine = Cl, Zinc = Zn
• Some come from Latin/Greek/German names — Iron = Fe (Latin ferrum), Mercury = Hg (Greek hydrargyros), Tungsten = W (German wolfram)

5. Atomic Number, Mass Number & Notation

Standard notation for an atom:

5.1 Bohr–Bury Rules for Electron Distribution

• Maximum electrons in a shell $= 2n^2$ (where $n$ = shell number): K-shell ($n=1$) → 2; L-shell ($n=2$) → 8; M-shell ($n=3$) → 18
• Maximum electrons in the outermost shell = 8 (except when it’s the only shell, which holds max 2)
• Shells fill stepwise from innermost outward (K → L → M → N…); a shell fills completely before the next one starts

6. Valency — Combining Capacity

Valency = number of electrons an atom gains, loses, or shares to complete its octet (achieve stability).

Exactly 4 valence electrons (e.g., Carbon: 2, 4) → tends to share 4 electrons → valency 4.

7. Isotopes and Isobars

7.1 Isotopes

Isotopes are atoms of the same element (same atomic number $Z$, same number of protons/electrons) but with different numbers of neutrons, hence different mass numbers $A$.

Applications of Isotopes

• $^{235}_{92}\text{U}$ — fuel in nuclear reactors (electricity generation)
• $^{60}_{27}\text{Co}$ — radiotherapy for cancer treatment
• $^{131}_{53}\text{I}$ — treatment of goitre and thyroid cancer
• $^{14}_{6}\text{C}$ — radiocarbon dating of fossils/artefacts in archaeology and geology

Average (Weighted) Atomic Mass

Since isotopes don’t occur in equal proportions, the atomic mass of an element is calculated as a weighted average, not a simple average.

7.2 Isobars

Isobars are atoms of different elements with the same mass number but different atomic numbers.

8. Beyond Bohr — The Modern View

Bohr’s model, too, was eventually found incomplete. Electrons do not follow fixed, well-defined circular paths. The modern quantum mechanical model describes electrons as existing in “electron clouds” — regions around the nucleus where an electron is most likely to be found, rather than an exact, predictable path. (Detailed treatment is reserved for higher grades.)

9. Scientists to Remember

10. Exam Question Bank

A. MCQ / Assertion–Reason (1 mark each)

B. Short Answer (2–3 marks)

C. Numerical Problems

D. Long Answer / HOTS (4–5 marks)

1. Introduction — The Idea of a Tissue

A tissue is a group of cells that are similar in structure and work together to perform a specific function. The formation of tissues creates division of labour in the body, which increases efficiency and allows complex life processes to occur.

In unicellular organisms (e.g., Amoeba), a single cell performs all life functions. In multicellular organisms (plants and animals), different groups of specialised cells carry out different functions — this is why tissues exist.

Why Are Plant and Animal Tissues Different?

2. Tissues for Growth in Plants

Plants grow in three distinct ways:

• Increase in length — height of stem and depth of roots
• Increase in girth — thickness of the stem
• Regrowth — after cutting of branches or grazing by animals

All three types of growth depend on actively dividing cells, collectively called meristematic tissue. There are three types, based on location and function.

2.1 Apical Meristem — Growth in Length

This growth zone at the tips of roots and shoots is called the apical meristem. It is responsible for increase in length of the plant.

2.2 Lateral Meristem — Growth in Girth

Located along the circumference of the stem (in a ring), this meristem produces new cells inside and outside in a concentric manner, increasing the stem’s diameter. This is called the lateral meristem (also linked to formation of annual growth rings seen in a cut tree trunk).

2.3 Intercalary Meristem — Regrowth After Cutting

Located at the base of the internode, or just above a node (the point where branches/leaves arise). When the tip of a stem is cut, growth in length stops, but new branches sprout from the nodes — this is why hedges become bushier after trimming and grass regrows after mowing/grazing.

Characteristics of Meristematic Cells

• Small in size, with thin cell walls
• Large, prominent nucleus and dense cytoplasm rich in organelles
• Vacuoles generally absent
• Tightly packed with little/no intercellular space

These features allow rapid and continuous cell division.

3. Permanent Tissues in Plants

Permanent tissues are classified as:

• Simple — composed of only one type of cell (parenchyma, collenchyma, sclerenchyma)
• Complex — composed of more than one type of cell working together (xylem, phloem)

3.1 Protective Tissue — Epidermis

The epidermis is the outermost layer of the plant body — a single, tightly packed layer of flat, rectangular cells. It is covered by a waxy layer called the cuticle, which reduces water loss. In roots, epidermal projections form root hairs that increase surface area for water/mineral absorption. In leaves, the epidermis contains pores called stomata, which allow gaseous exchange and transpiration (evaporation of water vapour), creating a transpiration pull that helps move water up through the xylem.

3.2 Supporting Tissues (Simple Permanent Tissues)

3.3 Conducting Tissues (Complex Permanent Tissues)

3.4 Plant Tissue Systems

All plant tissues are organised into three larger tissue systems:

1. Dermal tissue system — outer covering; protects and reduces water loss (epidermis)
2. Ground tissue system — main body between dermal and vascular tissue; includes parenchyma, collenchyma, sclerenchyma
3. Vascular tissue system — conducting tissues: xylem and phloem

4. Animal Tissues

Animal tissues are broadly of four types: Epithelial, Connective, Muscular, and Nervous.

4.1 Epithelial Tissue

Forms the outer covering of the body (skin) and lines internal organs (mouth, lungs, blood vessels, intestine). Cells are closely packed with minimal intercellular space, preventing entry of germs and reducing water loss.

4.2 Connective Tissue

Connects and supports other tissues/organs. Composition varies in the matrix (the substance between cells) — from fluid (blood) to hard (bone).

Components of Blood

• Plasma — fluid part (~55% of volume); carries dissolved substances
• RBCs (Red Blood Cells) — contain haemoglobin (iron-rich protein, gives red colour); lifespan ~4 months
• WBCs (White Blood Cells) — fight infection; collect at infected sites causing pus/inflammation
• Platelets — help in blood clotting at injury sites

4.3 Muscular Tissue

4.4 Nervous Tissue

Forms the body’s control and coordination network. Made up of neurons (nerve cells), specialised to receive, process, and transmit messages.

Structure of a Neuron (label carefully for diagram questions)

• Cell body — contains nucleus; controls cell activities
• Dendrites — receive signals from other neurons
• Axon — long fibre carrying messages away from the cell body, ending in axon terminals that transmit signals to other cells

5. The Musculoskeletal System

Made up of bones, muscles, joints, cartilage, tendons, and ligaments. It helps the body stand upright, move, maintain posture, and protect delicate organs — functioning under control of the nervous system. Muscles pull on bones via tendons; muscle contraction → tendon transmits force → movement at a joint.

5.1 Types of Joints

5.2 Skeletal System — Backbone & Rib Cage

• Vertebral column (backbone) — series of small bones called vertebrae; supports the body, allows upright posture. Cartilage discs between vertebrae cushion and allow flexibility while protecting the spinal cord.
• Rib cage — 12 pairs of ribs; attached to the spine (back) and sternum/breast bone (front) via flexible cartilage. This flexibility allows the rib cage to expand/contract during breathing.

6. Important Named Concepts & Scientists

7. Exam Question Bank

A. Multiple Choice / Assertion-Reason (1 mark each)

B. Short Answer (2–3 marks)

C. Long Answer / HOTS (4–5 marks)

D. Numerical / Graph-Based