📘 HC Verma Vol 1 — Chapter 1: Introduction to Physics 🔰 Fully JEE-Oriented Format ───────────────────────────────────────────────🟩 CONCEPT 1: What is Physics? Theory Summary:- Physics is the study of nature’s laws and their mathematical expression.- It explains phenomena from atomic to cosmic scale.- Based on observation, experiments, and logic.- Forms the foundation of all engineering and technology. Important Formulas + Units: | Quantity | Formula | SI Unit | Dimensions ||----------------|------------------|-----------|--------------------|| Speed | v = d / t | m/s | [L T⁻¹] || Force | F = m · a | N | [M L T⁻²] || Work/Energy | W = F · d | J | [M L² T⁻²] || Power | P = W / t | W | [M L² T⁻³] | Numericals: Q1. A force of 20 N is applied on an object and it moves 3 m. Find the work done. Q2. A body of mass 5 kg accelerates at 4 m/s². Find the force. Q3. A 60 W bulb runs for 2 hours. Find the energy consumed. Solutions: Q1. W = F × d = 20 × 3 = 60 J Q2. F = m × a = 5 × 4 = 20 N Q3. E = P × t = 60 × (2 × 3600) = 432000 J = 432 kJ ───────────────────────────────────────────────🟩 CONCEPT 2: Fundamental Forces of Nature Theory Summary:- Four fundamental forces in nature: | Force Type | Acts Between | Relative Strength ||-------------------|------------------------------------|-------------------|| Gravitational | All masses | 10⁻³⁹ || Electromagnetic | Charged particles | 10⁻² || Strong Nuclear | Protons and neutrons in nucleus | 1 (Strongest) || Weak Nuclear | During beta decay | 10⁻¹³ |

• Gravitational and electromagnetic forces are long-range. - Strong and weak nuclear forces are short-range. Units & Dimensions: | Quantity | SI Unit | Dimensions ||--------------------|-------------|--------------------|| Gravitational Force| N | [M L T⁻²] || Charge | C | [A T] || Electric Force | N | [M L T⁻²] | Numericals: Q1. Find gravitational force between two 5 kg masses placed 2 m apart. Take G = 6.67 × 10⁻¹¹ Nm²/kg² Q2. Compare gravitational and electrostatic force between a proton and electron placed 1 nm apart. Take e = 1.6 × 10⁻¹⁹ C, ε₀ = 8.85 × 10⁻¹² Solutions: Q1. F = G·m₁·m₂ / r² = (6.67 × 10⁻¹¹ × 5 × 5) / (2)² = 4.17 × 10⁻¹⁰ N Q2. Gravitational Force is very small. Electrostatic Force = (1 / 4πε₀) × (e² / r²) Electrostatic force ≫ Gravitational force ⇒ Electrostatic force dominates at atomic scale. ───────────────────────────────────────────────🟩 CONCEPT 3: Units and Dimensions Theory Summary:- Physical quantities are either fundamental or derived.- 7 Base SI quantities: Length (m), Mass (kg), Time (s), Current (A), Temperature (K), Luminous Intensity (cd), Amount of Substance (mol)- Derived quantities are expressed using base ones.- Dimensions show dependency on base units. Important Formulas + Units: | Quantity | Formula | SI Unit | Dimensions ||----------------|---------------------|-----------|--------------------|| Speed | v = d / t | m/s | [L T⁻¹] || Acceleration | a = v / t | m/s² | [L T⁻²] || Force | F = m · a | N | [M L T⁻²] || Work | W = F · d | J | [M L² T⁻²] || Power | P = W / t | W | [M L² T⁻³] || Pressure | P = F / A | Pa | [M L⁻¹ T⁻²] | Numericals: Q1. A quantity X is defined as: X = (Force × Distance) / Velocity Find the dimensions of X. Q2. Check if the equation is dimensionally correct: v² = u² + 2as Q3. Derive formula for time period T of a pendulum (depends on length l and g) using dimensional analysis. Solutions: Q1. Force = [M L T⁻²], Distance = [L], Velocity = [L T⁻¹] X = ([M L T⁻²] × [L]) / [L T⁻¹] = [M L² T⁻²] / [L T⁻¹] = [M L T⁻¹] Q2. LHS: [L² T⁻²], RHS: [L² T⁻²] + [L² T⁻²] ⇒ Dimensions match ⇒ Equation is correct. Q3. Assume: T ∝ lᵃ · gᵇ T = [T], l = [L], g = [L T⁻²] So, [T] = [Lᵃ] × [Lᵇ T⁻²ᵇ] = [L^(a + b) T⁻²ᵇ] Equating: a + b = 0, -2b = 1 → b = -½, a = ½ ⇒ T ∝ √(l / g)

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