A man measures a rod’s length as 1.50 m using a metre rule. If the actual length is 1.52 m, what is the percentage error?
Absolute error = |1.50 - 1.52| = 0.02 m. Percentage error = (error / actual length) × 100 = (0.02 / 1.52) × 100 ≈ 1.32%.
A machine lifts a 400 N load through 5 m in 10 s with 80% efficiency. What is the power input to the machine?
Work output = force × distance = 400 × 5 = 2000 J. Power output = work / time = 2000 / 10 = 200 W. Efficiency = (power output / power input) × 100 → 80 = (200 / P_in) × 100 → P_in = 200 / 0.8 = 250 W.
A simple pendulum has a period of 1.5 s on Earth. What is its period on the Moon, where gravitational acceleration is 1/6 that of Earth?
Period T = 2π√(L/g). On the Moon, g_moon = g_earth / 6. T_moon / T_earth = √(g_earth / g_moon) = √6 ≈ 2.45. T_moon = 1.5 × 2.45 ≈ 3.67 s.
A 2 kg body moving at 5 ms^-1 collides inelastically with a 3 kg body at rest. What is their common velocity after collision?
Conservation of momentum: m1u1 + m2u2 = (m1 + m2)v. 2 × 5 + 3 × 0 = (2 + 3)v → 10 = 5v → v = 2 ms^-1.
A wheel of radius 0.2 m rotates at 10 revolutions per second. What is the linear speed of a point on its rim?
Angular speed ω = 2πf = 2π × 10 = 20π rad/s. Linear speed v = ωr = 20π × 0.2 ≈ 12.56 ms^-1.
A 5 kg body is immersed in a liquid of density 800 kgm^-3 with a volume of 0.002 m^3. What is its apparent weight? (g = 10 ms^-2)
Actual weight = mg = 5 × 10 = 50 N. Upthrust = ρVg = 800 × 0.002 × 10 = 16 N. Apparent weight = actual weight - upthrust = 50 - 16 = 34 N.
A gas at 0°C and 1 atm occupies 500 cm^3. What is its volume at 100°C and 2 atm?
Using (P1V1)/T1 = (P2V2)/T2: T1 = 273 K, T2 = 373 K. (1 × 500) / 273 = (2 × V2) / 373 → V2 = (500 × 373) / (273 × 2) ≈ 341 cm^3.
The specific latent heat of vaporization of a liquid is 2.26 × 10^6 Jkg^-1. How much heat is required to vaporize 0.2 kg at its boiling point?
Heat Q = mL = 0.2 × 2.26 × 10^6 = 4.52 × 10^5 J.
The second harmonic frequency of a string fixed at both ends is 300 Hz. What is the fundamental frequency?
Second harmonic f_2 = 2f_1. 300 = 2f_1 → f_1 = 300 / 2 = 150 Hz.
An object is placed 30 cm in front of a concave mirror with a focal length of 20 cm. What is the magnification of the image?
Using 1/f = 1/u + 1/v: 1/20 = 1/30 + 1/v → 1/v = 1/20 - 1/30 = 1/60 → v = 60 cm. Magnification m = -v/u = -60/30 = -2 (magnitude = 2).
A convex lens of focal length 25 cm forms a real image at 50 cm. What is the object distance?
Using 1/f = 1/u + 1/v: 1/25 = 1/u + 1/50 → 1/u = 1/25 - 1/50 = 1/50 → u = 50 cm.
The refractive index of a medium is 1.6, and the speed of light in air is 3 × 10^8 ms^-1. What is the speed in the medium?
Refractive index n = c/v. 1.6 = (3 × 10^8) / v → v = (3 × 10^8) / 1.6 = 1.875 × 10^8 ms^-1.
A prism has a minimum deviation angle of 40° and an apex angle of 60°. What is the refractive index of the prism material?
At minimum deviation, δ_m = (n - 1)A. 40 = (n - 1) × 60 → n - 1 = 40/60 = 2/3 → n = 1 + 2/3 = 1.5.
A 5 × 10^-6 C charged particle moves at 2 ms^-1 perpendicular to a 0.3 T magnetic field. What is the force on the particle?
Force F = qvB sinθ. θ = 90°, sinθ = 1. F = (5 × 10^-6) × 2 × 0.3 = 3.0 × 10^-5 N.
Three resistors of 4 Ω, 6 Ω, and 12 Ω are connected in parallel. What is the equivalent resistance?
1/Req = 1/4 + 1/6 + 1/12 = (3 + 2 + 1)/12 = 6/12 = 0.5. Req = 1 / 0.5 = 2 Ω.
A 1000 W electric heater operates at 220 V. What is the resistance of the heater?
Power P = V^2 / R. R = V^2 / P = (220)^2 / 1000 = 48,400 / 1000 = 48.4 Ω.
A 0.5 m wire carrying 3 A is placed at 30° to a 0.8 T magnetic field. What is the force on the wire?
Force F = BIL sinθ. B = 0.8 T, I = 3 A, L = 0.5 m, θ = 30°, sin30° = 0.5. F = 0.8 × 3 × 0.5 × 0.5 = 0.6 N.
In a nuclear reaction, two light nuclei combine to form a heavier nucleus. This process is an example of
Fusion involves the combination of light nuclei (e.g., hydrogen) to form a heavier nucleus, releasing energy, as in stars.
A metal’s work function is 2.5 eV. What is the maximum kinetic energy of an emitted electron if the incident light’s frequency is 7.6 × 10^14 Hz? (h = 6.63 × 10^-34 Js, 1 eV = 1.6 × 10^-19 J)
Photon energy E = hf = (6.63 × 10^-34) × (7.6 × 10^14) ≈ 5.04 × 10^-19 J = (5.04 × 10^-19) / (1.6 × 10^-19) ≈ 3.15 eV. Max KE = E - φ = 3.15 - 2.5 = 0.65 eV ≈ 0.5 eV.
A particle moving at 2 × 10^6 ms^-1 has a de Broglie wavelength of 3.315 × 10^-11 m. What is its mass? (h = 6.63 × 10^-34 Js)
λ = h / (mv). m = h / (λv) = (6.63 × 10^-34) / (3.315 × 10^-11 × 2 × 10^6) = 1.0 × 10^-30 kg.
Which of the following is a characteristic of gamma rays?
Gamma rays are electromagnetic waves with high energy and penetrating power, unaffected by magnetic fields.
A 0.5 kg ball is thrown vertically upwards at 12 ms^-1. What is its potential energy at maximum height? (g = 10 ms^-2)
At max height, PE = initial KE. KE = (1/2)mv^2 = (1/2) × 0.5 × (12)^2 = 36 J. PE = 36 J.
The fundamental frequency of a closed pipe is 200 Hz. If the speed of sound is 340 ms^-1, what is the pipe’s length?
For a closed pipe, f = v / (4L). 200 = 340 / (4L) → 4L = 340 / 200 → L = 0.425 m ≈ 0.43 m.
An object is placed 10 cm in front of a convex lens of focal length 15 cm. What is the nature of the image?
1/f = 1/u + 1/v. 1/15 = 1/10 + 1/v → 1/v = 1/15 - 1/10 = -1/30 → v = -30 cm (virtual). Image is virtual and upright.
A microscope has an objective lens of focal length 2 cm and an eyepiece of focal length 5 cm. If the lens distance is 18 cm, what is the magnification?
Magnification M = (v_o / u_o) × (D / f_e). Objective: 1/2 = 1/u_o + 1/(18-5) → u_o ≈ 2.6 cm, v_o ≈ 13 cm, m_o = 13 / 2.6 = 5. Eyepiece: m_e = D / f_e = 25 / 5 = 5 (D = 25 cm). M = 5 × 5 = 25.
A charged particle moves at 60° to a magnetic field. If the force is 3 × 10^-3 N, charge is 2 × 10^-6 C, and speed is 5 ms^-1, what is the field strength?
F = qvB sinθ. F = 3 × 10^-3 N, q = 2 × 10^-6 C, v = 5 ms^-1, θ = 60°, sin60° ≈ 0.866. B = F / (qv sinθ) = (3 × 10^-3) / (2 × 10^-6 × 5 × 0.866) ≈ 0.4 T.
A 12 V battery is connected to 4 Ω and 8 Ω resistors in series. What is the potential difference across the 8 Ω resistor?
Total resistance = 4 + 8 = 12 Ω. Current I = V/R = 12 / 12 = 1 A. Voltage across 8 Ω = I × R = 1 × 8 = 8 V.
A household consumes 10 kWh of energy in 5 hours. What is the average power consumption?
Power = energy / time = 10 kWh / 5 h = 2 kW.
Which of the following is NOT a property of electromagnetic waves?
Electromagnetic waves propagate through a vacuum and do not require a medium, unlike mechanical waves.
A radioactive substance has a half-life of 8 days. How long will it take for 75% to decay?
75% decay means 25% remains. 25% = (1/2)^n → (1/2)^2 = 1/4. n = 2 half-lives. Time = 2 × 8 = 16 days.
Which particle has the highest penetrating power?
Gamma rays, being electromagnetic waves, have high penetrating power, passing through most materials.
A metal’s threshold wavelength is 600 nm. What is its work function? (h = 6.63 × 10^-34 Js, c = 3 × 10^8 ms^-1)
Work function φ = hc/λ. λ = 6 × 10^-7 m. φ = (6.63 × 10^-34 × 3 × 10^8) / (6 × 10^-7) ≈ 3.3 × 10^-19 J.
A p-n junction diode allows current to flow easily when
Forward bias reduces the potential barrier in a p-n junction, allowing current to flow easily.
The specific heat capacity of water is 4200 Jkg^-1K^-1. How much heat is needed to raise 2 kg of water from 20°C to 50°C?
Heat Q = mcΔθ = 2 × 4200 × (50 - 20) = 2 × 4200 × 30 = 252,000 J.
A 10 kg object accelerates from rest to 5 ms^-1 in 4 s. What is the average power delivered?
Work = ΔKE = (1/2)mv^2 = (1/2) × 10 × (5)^2 = 125 J. Power = work / time = 125 / 4 = 125 W.
Which of the following is a characteristic of beta particles?
Beta particles are high-energy electrons, negatively charged, with moderate penetrating power.
A wave has a frequency of 500 Hz and a wavelength of 0.68 m. What is its speed?
Speed v = fλ = 500 × 0.68 = 340 ms^-1.
An AC circuit has a frequency of 50 Hz. What is its time period?
Time period T = 1/f = 1/50 = 0.02 s.
The wave-particle duality of light explains
Wave-particle duality explains light’s particle nature (photoelectric effect) and wave nature (diffraction).
The resistance of a semiconductor typically
In semiconductors, increased temperature excites more charge carriers, reducing resistance.
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