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(9d) (i) Bulk modulus Bulk modulus is a measure of a material's resistance to compression under uniform pressure. (ii) Energy gained by the wire Given: Mass (m) = 2.5g = 0.0025kg Extension (x) = 2cm = 0.02m g = 10m/s² Force (F) = mg = 0.0025 × 10 = 0.025N Energy gained (E) = (1/2)Fx = (1/2) × 0.025 × 0.02 = 2.5 × 10⁻⁴ J =========================== (10a) (i) First overtone; The first overtone is the second harmonic of a vibrating system, having a frequency twice that of the fundamental frequency. (ii) End correction; End correction accounts for the fact that the antinode of a standing wave in a pipe doesn't exactly coincide with the physical end. (10b) Given: Length (L) = 40 cm = 0.4 m End correction (e) = 3.2 cm = 0.032 m Velocity of sound (v) = 330 m/s Effective length = L + e = 0.4 + 0.032 = 0.432m Wave length (λ)= 4Leff λ = 4×0.432 = 1.728m Frequency (f) = v/λ= = 330/1.728 = 191Hz (10ci) Given: n = 8 n = 360° / β - 1 360° / β = n + 1 360° / β = 8 + 1 360° / β = 9 β = 360° / 9 β = 40° (10cii) (i) Mirage involves refraction and total internal reflection in air, while total internal reflection occurs at a medium boundary. (ii) Mirage produces an inverted image, while total internal reflection produces a mirror-like reflection. (10ciii) Given: f₀ = 3 cm, fe = 6 cm, L = 20 cm v₀ = L - fe = 20 - 6 = 14 cm 1/f₀ = 1/v₀ - 1/u₀ 1/3 = 1/14 - 1/u₀ 1/u₀ = 1/14 - 1/3 1/u₀ = (3 - 14) / 42 1/u₀ = -11 / 42 u₀ = -42 / 11 u₀ = -3.82 cm ===========================(9d) (i) Bulk modulus Bulk modulus is a measure of a material's resistance to compression under uniform pressure. (ii) Energy gained by the wire Given: Mass (m) = 2.5g = 0.0025kg Extension (x) = 2cm = 0.02m g = 10m/s² Force (F) = mg = 0.0025 × 10 = 0.025N Energy gained (E) = (1/2)Fx = (1/2) × 0.025 × 0.02 = 2.5 × 10⁻⁴ J =========================== (10a) (i) First overtone; The first overtone is the second harmonic of a vibrating system, having a frequency twice that of the fundamental frequency. (ii) End correction; End correction accounts for the fact that the antinode of a standing wave in a pipe doesn't exactly coincide with the physical end. (10b) Given: Length (L) = 40 cm = 0.4 m End correction (e) = 3.2 cm = 0.032 m Velocity of sound (v) = 330 m/s Effective length = L + e = 0.4 + 0.032 = 0.432m Wave length (λ)= 4Leff λ = 4×0.432 = 1.728m Frequency (f) = v/λ= = 330/1.728 = 191Hz (10ci) Given: n = 8 n = 360° / β - 1 360° / β = n + 1 360° / β = 8 + 1 360° / β = 9 β = 360° / 9 β = 40° (10cii) (i) Mirage involves refraction and total internal reflection in air, while total internal reflection occurs at a medium boundary. (ii) Mirage produces an inverted image, while total internal reflection produces a mirror-like reflection. (10ciii) Given: f₀ = 3 cm, fe = 6 cm, L = 20 cm v₀ = L - fe = 20 - 6 = 14 cm 1/f₀ = 1/v₀ - 1/u₀ 1/3 = 1/14 - 1/u₀ 1/u₀ = 1/14 - 1/3 1/u₀ = (3 - 14) / 42 1/u₀ = -11 / 42 u₀ = -42 / 11 u₀ = -3.82 cm ===========================9bii) Slope = ∆F/∆e Point 1: (Extension = 10.0 cm, Force = 2.0 N) Point 2: (Extension = 30.0 cm, Force = 6.0 N) S = (6.0-2.0)/(30.0-10.0) S = 4.0/20.0 S = 0.2N/cm (9biii) The slope represents the spring constant k, indicating the stiffness of the spring. (9c) Given: Mass (m) = 40 g = 0.04 kg Elastic constant (k) = 350 N/m Extension (x) = 4 cm = 0.04 m Elastic potential energy stored in the rubber(E) = (1/2)kx² = (1/2) × 35 × (0.04)² (1/2) × 35 × 0.0016 = 0.28 J This energy is converted to kinetic energy of the stone: K = (1/2)mv² = E (1/2)mv² = 0.28 J (1/2) × 0.04 × v² = 0.28 v² = (2 × 0.28)/0.04 v² = 14 v = √14 v = 3.74 m/s (9d) (i) Bulk modulus Bulk modulus is a measure of a material's resistance to compression under uniform pressure. (ii) Energy gained by the wire Given: Mass (m) = 2.5g = 0.0025kg Extension (x) = 2cm = 0.02m g = 10m/s² Force (F) = mg = 0.0025 × 10 = 0.025N Energy gained (E) = (1/2)Fx = (1/2) × 0.025 × 0.02 = 2.5 × 10⁻⁴ J

WAEC Examrunz 2025: PHYSICS-OBJ 01-10: BBCDACBCBB 11-20: ADBBCCDCBC 21-30: CDABAAADBA 31-40: ABABCCBCDA 41-50: BBACBBCABC Solved Completed!!! ========================= PHYSICS- ESSAY-ANSWERS PART I: ANSWER FIVE (5) QUESTIONS ONLY (1) R = (U²Sin2θ)/g Where: -U is the initial velocity (dimension: LT⁻¹, where L is length and T is time) -θ is the angle (dimensionless) -g is the acceleration due to gravity (dimension: LT⁻²) Now, let's determine the dimension of R: R = (U²Sin2θ)/g R = U²/g = ((LT⁻¹)² / (LT⁻²) = (L²T⁻²) / (LT⁻²) = L =========================== (2) (i) Gas Laser: Used in barcode scanners in supermarkets and retail stores. (ii) Chemical Laser: Used in military applications for missile defense and high-energy laser weapons. (iii) Dye Laser: Used in medical treatments such as removing birthmarks and vascular skin lesions. =========================== =========================== (5) Given: Initial extension = 0.04 m when F = 6 N spring constant (k): k = F /e = 6 N / 0.04 m = 150 N/m New extension when F = 8 N: e = F / k = 8 N/150 N/m = 0.0533 m New length = Natural length + New extension = 5 m + 0.0533 m = 5.0533 m =========================== (6) (i) Laser light consists of a single wavelength, whereas white light comprises multiple wavelengths. (ii) Laser light waves are in phase (coherent), whereas white light waves are out of phase (incoherent). (iii) Laser light travels in a focused, directional beam, whereas white light disperses in various directions. =========================== (7) (i) Retentivity Retentivity is the ability of a magnetic material to retain its magnetization even after the external magnetic field is removed. (ii) Iron =========================== PART II: ANSWER THREE(3) QUESTIONS ONLY (8ai) A semiconductor is said to be doped when a small amount of impurity is intentionally added to a pure semiconductor to increase its electrical conductivity. (8aii) I. Intrinsic semiconductor: An intrinsic semiconductor is a pure semiconductor material without any significant impurities added. II. Extrinsic semiconductor: An extrinsic semiconductor is a semiconductor that has been doped with impurity atoms (dopants) to increase its conductivity. (8c) Given: Wavelength (λ) = 3.0 × 10⁻⁷ m Kinetic energy (KE) = 1.5 × 10⁻¹⁹ J c = 3.0 × 10⁸ m/s mₑ = 9.1 × 10⁻³¹ kg h = 6.6 × 10⁻³⁴ Js (i) Maximum velocity of the photoelectron KE = (1/2)mv² 1.5 × 10⁻¹⁹ J = (1/2) × 9.1 × 10⁻³¹ kg × v² v² = 2 × 1.5 × 10⁻¹⁹ J / (9.1 × 10⁻³¹ kg) v² = 3.3 × 10¹¹ v = √(3.3 × 10¹¹) v ≈ 5.74 × 10⁵ m/s (ii) Work function of the metal E = hc / λ = (6.6 × 10⁻³⁴ Js × 3.0 × 10⁸ m/s) / (3.0 × 10⁻⁷ m) = 6.6 × 10⁻¹⁹ J Work function (φ) = E - KE = 6.6 × 10⁻¹⁹ J - 1.5 × 10⁻¹⁹ J = 5.1 × 10⁻¹⁹ J (8d) Stopping potential is defined as the minimum negative potential (voltage) applied to the collector electrode in a photoelectric experiment that just stops the most energetic photoelectrons emitted from reaching the collector. =========================== (9a) Deformation refers to the change in shape or size of an object under an external force, while elasticity refers to the ability of an object to return to its original shape or size after the external force is removed. (9bii) Slope = ∆F/∆e Point 1: (Extension = 10.0 cm, Force = 2.0 N) Point 2: (Extension = 30.0 cm, Force = 6.0 N) S = (6.0-2.0)/(30.0-10.0) S = 4.0/20.0 S = 0.2N/cm (9biii) The slope represents the spring constant k, indicating the stiffness of the spring. (9c) Given: Mass (m) = 40 g = 0.04 kg Elastic constant (k) = 350 N/m Extension (x) = 4 cm = 0.04 m Elastic potential energy stored in the rubber(E) = (1/2)kx² = (1/2) × 35 × (0.04)² (1/2) × 35 × 0.0016 = 0.28 J This energy is converted to kinetic energy of the stone: K = (1/2)mv² = E (1/2)mv² = 0.28 J (1/2) × 0.04 × v² = 0.28 v² = (2 × 0.28)/0.04 v² = 14 v = √14 v = 3.74 m/s

NECO BECE MATHS PART 2 01-10: ACCBCCBCEC 11-20: DBCEDAAEDD 21-30: CDCECECCAC 31-40: ADCBAADABA 41-50: ECDBCCBCCA 51-60: DCDCDDCBCC COMPLETED

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Physics no 8
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