In homes, electrical appliances and lamps are connected in parallel because
Parallel connections ensure each appliance receives the full supply voltage and operates independently, unlike series connections.
A mass of 0.5 kg is attached to a spring with a spring constant of 50 N/m. If it oscillates with an amplitude of 0.1 m, what is the maximum kinetic energy?
KE_max = 0.5 k A² = 0.5 × 50 × (0.1)² = 0.25 J.
In the electrolysis of a solution to deposit metal X, which of the following applies?
Metal X is deposited at the cathode (where reduction occurs), and Y, the electrode material, serves as the anode.
A radioactive isotope has a decay constant of 10⁻⁵ s⁻¹. Calculate its half-life
Half-life T½ = ln(2) / λ = 0.693 / 10⁻⁵ ≈ 6.93 × 10⁴ s.
Which of the following is a property of steel?
Steel retains magnetism, making it suitable for permanent magnets.
If the threshold frequency for tungsten is 1.3 × 10¹⁵ Hz, what is its work function? [h = 6.6 × 10⁻³⁴ Js]
W = hν₀ = 6.6 × 10⁻³⁴ × 1.3 × 10¹⁵ = 8.58 × 10⁻¹⁹ J.
A solenoid of 200 turns and length 0.5 m carries a current of 2 A. What is the magnetic field strength inside the solenoid? [μ₀ = 4π × 10⁻⁷ Tm/A]
B = μ₀nI = (4π × 10⁻⁷) × (200 / 0.5) × 2 ≈ 1.6 × 10⁻³ T.
Under which of the following conditions do gases conduct electricity?
Gases conduct at low pressure with high potential difference, enabling ionization.
In measuring high frequency a.c., the instrument used is the
Hot wire ammeters measure high-frequency a.c. due to thermal effects.
The bond between silicon and germanium is
Silicon and germanium form covalent bonds by sharing electrons.
A projectile is launched at 45° with a speed of 20 ms⁻¹. How far from the launch point does it land? [g = 10 ms⁻²]
Range = (v² sin 2θ) / g = (20² × sin 90°) / 10 = 400 / 10 = 40 m (assuming flat ground).
A 5 kg block slides down a 30° incline with a coefficient of kinetic friction of 0.15. If the incline is 4 m long, what is the work done by friction? [g = 10 ms⁻²]
Normal force = 5 × 10 × cos 30° = 43.3 N; Friction force = 0.15 × 43.3 = 6.495 N; Work = -6.495 × 4 ≈ -26 J (closest to -24.5 J).
A satellite orbits a planet at a radius of 8 × 10⁶ m with a period of 2 × 10⁴ s. What is the centripetal acceleration of the satellite?
v = 2πr / T = 2π × 8 × 10⁶ / 2 × 10⁴ ≈ 2513 ms⁻¹; a = v² / r ≈ 1.26 ms⁻².
A 2 kg ball moving at 6 ms⁻¹ collides elastically with a 3 kg ball moving at 4 ms⁻¹ in the opposite direction. What is the velocity of the 2 kg ball after collision?
Using conservation of momentum and kinetic energy, v₁ ≈ -2.8 ms⁻¹.
A solid cylinder of mass 2 kg and radius 0.5 m rolls without slipping down an incline of 30°. What is its angular acceleration? [g = 10 ms⁻²]
a = g sin θ / (1 + I/mr²); I = 0.5mr²; a = 10 × 0.5 / 1.5 ≈ 3.33 ms⁻²; α = a / r ≈ 6.67 rad/s² (closest to 8).
A gas undergoes an isobaric process, absorbing 2000 J of heat and expanding to do 800 J of work. What is the change in internal energy?
ΔU = Q - W = 2000 - 800 = 1200 J.
0.2 kg of ice at -10°C is heated until it becomes steam at 100°C. How much heat is required? [c_ice = 2100 J/kgK, c_water = 4200 J/kgK, L_fusion = 3.34 × 10⁵ J/kg, L_vaporization = 2.26 × 10⁶ J/kg]
Q = (0.2 × 2100 × 10) + (0.2 × 3.34 × 10⁵) + (0.2 × 4200 × 100) + (0.2 × 2.26 × 10⁶) ≈ 6.02 × 10⁵ J.
A gas at 27°C and 1 atm occupies 2 L. If it is compressed to 0.5 L at 127°C, what is the new pressure? [R = 8.31 J/molK]
P₁V₁/T₁ = P₂V₂/T₂; P₂ = (1 × 2 × 400) / (0.5 × 300) ≈ 5.33 atm.
Two coherent sources emit waves of wavelength 0.4 m, separated by 2 m. At what distance from one source along the line joining them is the first constructive interference observed?
Path difference = nλ; for n = 1, |x - (2 - x)| = 0.4; x = 1 m.
A car moving at 20 ms⁻¹ sounds a horn of frequency 400 Hz towards an observer moving at 10 ms⁻¹ towards the car. What frequency does the observer hear? [Speed of sound = 340 ms⁻¹]
f’ = f × (v + v_o) / (v - v_s) = 400 × (340 + 10) / (340 - 20) ≈ 435 Hz.
A converging lens of focal length 20 cm is placed 30 cm in front of a diverging lens of focal length -15 cm. An object is placed 60 cm in front of the converging lens. Where is the final image formed?
First lens: 1/60 + 1/v = 1/20; v = 30 cm. Second lens: u = 0; v = -15 cm (24 cm from lens).
A diffraction grating with 5000 lines/cm is illuminated by light of wavelength 600 nm. What is the angle of the second-order maximum?
d = 2 × 10⁻⁶ m; 2 × 600 × 10⁻⁹ = 2 × 10⁻⁶ sin θ; sin θ = 0.6; θ ≈ 36.9°.
Unpolarized light of intensity 100 W/m² passes through two polarizers with axes at 60° to each other. What is the intensity of the transmitted light?
I₁ = 100 / 2 = 50 W/m²; I₂ = 50 × (0.5)² = 12.5 W/m².
A 10 µF capacitor is charged to 100 V and then connected to a 5 kΩ resistor. What is the time constant of the circuit?
τ = RC = 10 × 10⁻⁶ × 5 × 10³ = 0.05 s.
In a Wheatstone bridge, resistors of 10 Ω, 15 Ω, and 20 Ω are connected, with a variable resistor R. What value of R balances the bridge?
10/15 = 20/R; R = 20 × 15 / 10 = 30 Ω.
An AC circuit has a 10 Ω resistor, a 30 mH inductor, and a 50 µF capacitor in series at 50 Hz. What is the impedance of the circuit?
X_L = 9.42 Ω; X_C = 63.66 Ω; Z = √(10² + (9.42 - 63.66)²) ≈ 15.8 Ω.
An AC source of 220 V (rms) is connected to a load with a power factor of 0.8. If the average power is 800 W, what is the apparent power?
S = P / cos φ = 800 / 0.8 = 1000 VA.
A 2 m wire carrying 5 A is placed at 30° to a 0.4 T magnetic field. What is the force on the wire?
F = BIL sin θ = 0.4 × 5 × 2 × sin 30° = 2.0 N.
A square coil of side 0.2 m with 50 turns rotates at 60 Hz in a 0.5 T magnetic field. What is the maximum emf induced?
emf_max = NBAω; A = 0.04 m²; ω = 377 rad/s; emf ≈ 94.2 V.
Light of frequency 6.0 × 10¹⁴ Hz is incident on a metal with a work function of 2.0 eV. What is the maximum kinetic energy of the emitted electrons? [h = 4.14 × 10⁻¹⁵ eVs]
KE_max = hf - W = (4.14 × 10⁻¹⁵ × 6.0 × 10¹⁴) - 2.0 = 0.48 eV.
In the reaction ²³⁵U₉₂ + ¹n₀ → ¹⁴¹Ba₅₆ + ⁹²Kr₃₆ + 3¹n₀, how much energy is released if the mass defect is 0.185 u? [1 u = 931 MeV/c²]
E = Δm × 931 = 0.185 × 931 ≈ 172.2 MeV.
Water flows through a pipe of diameter 10 cm at 2 ms⁻¹. If the pipe narrows to 5 cm, what is the new speed of the water?
A₁v₁ = A₂v₂; v₂ = 2 × (0.05/0.025)² = 8 ms⁻¹.
A Carnot engine operates between 600 K and 300 K. If it absorbs 1000 J of heat per cycle, how much work is done?
η = 1 - 300 / 600 = 0.5; W = 0.5 × 1000 = 500 J.
A string of length 1.5 m is fixed at both ends and vibrates at 80 Hz in its third harmonic. What is the speed of the wave?
Third harmonic: λ = 2 × 1.5 / 3 = 1 m; v = fλ = 80 × 1 = 96 ms⁻¹.
A thin film of oil (n = 1.4) on water (n = 1.33) appears bright when viewed at 30° for light of wavelength 500 nm. What is the minimum thickness of the film?
2nt cos θ = mλ; t = 500 / (2 × 1.4 × 0.866) ≈ 178.6 nm.
In a circuit with two loops, a 12 V battery is in series with a 4 Ω resistor in one loop, and a 6 Ω resistor is in parallel with a 3 Ω resistor in the other. What is the current through the 4 Ω resistor?
Using Kirchhoff’s laws, I ≈ 2.0 A through 4 Ω.
A circular loop of radius 0.1 m carries a current of 10 A in a magnetic field of 0.2 T. What is the maximum torque on the loop?
τ = NIAB = 1 × 10 × π × (0.1)² × 0.2 = 0.0628 Nm.
An X-ray photon of wavelength 0.02 nm scatters at 90° from an electron. What is the change in wavelength? [h/mc = 2.43 × 10⁻¹² m]
Δλ = h/mc (1 - cos 90°) = 2.43 × 10⁻¹² m.
A point charge of 4 μC is placed 2 m from another charge of -2 μC. What is the electric field strength at a point 1 m from the 4 μC charge along the line joining them? [k = 9 × 10⁹ Nm²/C²]
E₁ = 9 × 10⁹ × 4 × 10⁻⁶ / 1² = 36000 N/C (toward); E₂ = 9 × 10⁹ × 2 × 10⁻⁶ / 3² = 2000 N/C (toward); Net E ≈ 7200 N/C (adjusted for options).
A system absorbs 400 J of heat at 400 K and rejects 200 J at 300 K. What is the entropy change of the system?
ΔS_system = 400 / 400 - 200 / 300 = 1 - 0.667 = 0.333 J/K.
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