A car accelerates uniformly from rest at 4 ms^-2 for 6 s, then moves at a constant velocity for 10 s. What is the total distance covered?
Distance during acceleration: s1 = (1/2)at^2 = (1/2) * 4 * 6^2 = 72 m. Velocity after 6 s: v = at = 4 * 6 = 24 ms^-1. Distance at constant velocity: s2 = v * t = 24 * 10 = 240 m. Total distance = 72 + 240 = 312 m.
A simple pendulum of length 0.4m has a period of 2s. What is the period of a similar pendulum of length 0.8m at the same place?
The period of a pendulum T = 2π√(L/g). T2/T1 = √(L2/L1) = √(0.8/0.4) = √2. T2 = 2 * √2 ≈ 2√2s.
A body of mass 2 kg moves with a velocity of 3 ms^-1. What is its momentum?
Momentum = mass * velocity = 2 * 3 = 6 kgms^-1.
A wave has a frequency of 500 Hz and a wavelength of 0.8 m. What is the speed of the wave?
Speed v = f * λ = 500 * 0.8 = 400 ms^-1.
A concave mirror has a radius of curvature of 20 cm. What is its focal length?
Focal length f = R/2. R = 20 cm, so f = 20 / 2 = 10 cm.
A cell of emf 1.8 V and internal resistance 0.2 Ω is connected to a 1.8 Ω resistor. What is the terminal voltage of the cell?
Total resistance = 1.8 + 0.2 = 2 Ω. Current I = E / (R + r) = 1.8 / 2 = 0.9 A. Terminal voltage V = E - Ir = 1.8 - (0.9 * 0.2) = 1.8 - 0.18 = 1.62 V ≈ 1.7 V.
A gas at 27°C and 2 x 10^5 Pa occupies 0.4 m^3. What is its volume at 127°C and 4 x 10^5 Pa?
Using the general gas law: (P1V1)/T1 = (P2V2)/T2. T1 = 27 + 273 = 300 K, T2 = 127 + 273 = 400 K. (2 x 10^5 * 0.4) / 300 = (4 x 10^5 * V2) / 400 → V2 = (0.4 * 300 * 4 x 10^5) / (400 * 2 x 10^5) = 0.24 m^3.
A body of mass 3 kg is dropped from a height of 20 m. What is its kinetic energy just before it hits the ground? (g = 10 ms^-2, neglect air resistance)
Potential energy at the top = mgh = 3 * 10 * 20 = 600 J. By conservation of energy, kinetic energy just before hitting the ground = 600 J.
A sound wave in air has a frequency of 680 Hz and a wavelength of 0.5 m. What is the temperature of the air? (Speed of sound at 0°C = 331 ms^-1)
Speed v = f * λ = 680 * 0.5 = 340 ms^-1. v = 331 * √(T/273). 340 / 331 = √(T/273) → (340/331)^2 = T/273 → T ≈ 293 K = 20°C.
A projectile is launched at 45° with a velocity of 40 ms^-1. What is the time to reach the maximum height? (g = 10 ms^-2)
Vertical component of velocity = v sinθ = 40 * sin45° = 40 * (√2/2) ≈ 28.3 ms^-1. Time to max height: t = (v sinθ) / g = 28.3 / 10 ≈ 2.83 s.
A block and tackle system has a velocity ratio of 5. If the efficiency of the system is 80%, what is the mechanical advantage?
Efficiency = (MA / VR) * 100. 80 = (MA / 5) * 100 → MA = (80 * 5) / 100 = 4.
A transformer has 500 turns in the primary coil and 2000 turns in the secondary coil. If the primary voltage is 120 V, what is the secondary voltage?
Vs/Vp = Ns/Np. Vs/120 = 2000/500 → Vs = 120 * 4 = 480 V.
A wooden block floats in water with 2/3 of its volume submerged. What is the density of the wood? (Density of water = 1000 kgm^-3)
Fraction submerged = density of wood / density of water. 2/3 = ρ / 1000 → ρ = (2/3) * 1000 = 667 kgm^-3.
A wave traveling along a string has a frequency of 400 Hz and a speed of 200 ms^-1. What is the phase difference between two points 0.25 m apart along the string?
Wavelength λ = v/f = 200 / 400 = 0.5 m. Phase difference = (2π/λ) * x = (2π/0.5) * 0.25 = 4π * 0.25 = π rad.
A radioactive substance has a half-life of 4 hours. What fraction of the substance remains after 12 hours?
Number of half-lives = 12 / 4 = 3. Fraction remaining = (1/2)^3 = 1/8.
A metal rod expands by 0.05 cm when heated from 25°C to 125°C. If its original length is 100 cm, what is its coefficient of linear expansion?
α = (ΔL / L) / ΔT. ΔL = 0.05 cm, L = 100 cm, ΔT = 125 - 25 = 100°C. α = (0.05 / 100) / 100 = 5 x 10^-5 K^-1.
A 0.5 kg piece of copper at 150°C is placed in 1 kg of water at 25°C. What is the final temperature? (c_copper = 400 Jkg^-1K^-1, c_water = 4200 Jkg^-1K^-1)
Heat lost by copper = heat gained by water. 0.5 * 400 * (150 - T) = 1 * 4200 * (T - 25). 200(150 - T) = 4200(T - 25) → 30,000 - 200T = 4200T - 105,000 → 135,000 = 4400T → T ≈ 30°C.
A conductor of length 0.4 m moves at 3 ms^-1 perpendicular to a magnetic field of 0.5 T. What is the induced emf in the conductor?
Induced emf = Blv = 0.5 * 0.4 * 3 = 0.6 V.
A capacitor of 10 μF is charged to 200 V. What is the charge stored in the capacitor?
Charge Q = CV = (10 x 10^-6) * 200 = 2 x 10^-3 C.
The de Broglie wavelength of an electron is 1.0 x 10^-10 m. What is its momentum? (h = 6.63 x 10^-34 Js)
de Broglie wavelength λ = h/p. p = h/λ = (6.63 x 10^-34) / (1.0 x 10^-10) = 6.63 x 10^-24 kgms^-1.
A 12 V battery with an internal resistance of 1 Ω is connected to a 5 Ω resistor. What is the current in the circuit?
Total resistance = 5 + 1 = 6 Ω. Current I = V / (R + r) = 12 / 6 = 2.0 A.
A force of 50 N extends a spring by 0.02 m. If a mass of 2 kg is hung on the spring, what is the extension? (g = 10 ms^-2)
Spring constant k = F/x = 50 / 0.02 = 2500 Nm^-1. Force by mass = mg = 2 * 10 = 20 N. Extension x = F/k = 20 / 2500 = 0.016 m.
A pipe open at both ends has a fundamental frequency of 250 Hz. If the speed of sound is 340 ms^-1, what is the length of the pipe?
For an open pipe, f = v / (2L). 250 = 340 / (2L) → 2L = 340 / 250 → L = (340 / 250) / 2 = 0.68 m.
A 500 W appliance operates at 250 V. How much energy does it consume in 2 hours?
Energy = power * time = 500 * 2 = 1000 Wh = 1.0 kWh.
A photon has an energy of 3.0 x 10^-19 J. What is its wavelength? (h = 6.63 x 10^-34 Js, c = 3 x 10^8 ms^-1)
E = hc/λ. λ = hc/E = (6.63 x 10^-34 * 3 x 10^8) / (3.0 x 10^-19) ≈ 6.63 x 10^-7 m ≈ 6.0 x 10^-7 m.
A body of mass 4 kg moves with a velocity of 6 ms^-1 and collides elastically with a stationary body of mass 2 kg. What is the velocity of the 2 kg body after collision?
For elastic collision, v2 = 2m1u1 / (m1 + m2) = (2 * 4 * 6) / (4 + 2) = 48 / 6 = 8 ms^-1.
A balloon filled with hydrogen has a volume of 2 m^3. If the density of air is 1.2 kgm^-3 and the density of hydrogen is 0.09 kgm^-3, what is the upthrust on the balloon? (g = 10 ms^-2)
Upthrust = weight of air displaced = ρ_air * V * g = 1.2 * 2 * 10 = 24 N.
A transformer steps down a voltage from 240 V to 24 V. If the primary coil has 600 turns, how many turns are in the secondary coil?
Vs/Vp = Ns/Np. 24/240 = Ns/600 → Ns = (24/240) * 600 = 60.
A wave has an amplitude of 0.02 m and a frequency of 50 Hz. If the speed of the wave is 25 ms^-1, what is the maximum transverse speed of a particle in the medium?
Max transverse speed = Aω = A * (2πf) = 0.02 * (2π * 50) = 0.02 * 314 ≈ 3.14 ms^-1.
A 0.3 kg block of iron at 500°C is dropped into 1 kg of water at 20°C. What is the final temperature? (c_iron = 450 Jkg^-1K^-1, c_water = 4200 Jkg^-1K^-1)
Heat lost by iron = heat gained by water. 0.3 * 450 * (500 - T) = 1 * 4200 * (T - 20). 135(500 - T) = 4200(T - 20) → 67,500 - 135T = 4200T - 84,000 → T ≈ 25°C.
A metal sphere of radius 0.05 m is heated from 20°C to 220°C. If the coefficient of volume expansion of the metal is 6 x 10^-5 K^-1, what is the increase in its volume?
Volume V = (4/3)πr^3 = (4/3)π(0.05)^3 ≈ 5.236 x 10^-4 m^3. ΔV = V * γ * ΔT = 5.236 x 10^-4 * (6 x 10^-5) * 200 ≈ 3.14 x 10^-6 m^3.
A pulley system has a velocity ratio of 6 and an efficiency of 75%. What effort is required to lift a load of 900 N?
Efficiency = (MA / VR) * 100. 75 = (MA / 6) * 100 → MA = 4.5. MA = load / effort → 4.5 = 900 / effort → effort = 900 / 4.5 = 200 N.
A string of length 0.8 m is fixed at both ends. If the speed of waves on the string is 400 ms^-1, what is the frequency of the third harmonic?
Fundamental frequency f_1 = v / (2L) = 400 / (2 * 0.8) = 250 Hz. Third harmonic f_3 = 3f_1 = 3 * 250 = 375 Hz.
A hydraulic press has a small piston of area 0.02 m^2 and a large piston of area 0.5 m^2. What force is exerted on the large piston if a force of 100 N is applied to the small piston?
Pressure = F1/A1 = F2/A2. 100 / 0.02 = F2 / 0.5 → F2 = (100 * 0.5) / 0.02 = 2500 N.
A gas is heated from 27°C to 127°C at constant volume. If the initial pressure is 1.5 x 10^5 Pa, what is the final pressure?
At constant volume, P1/T1 = P2/T2. T1 = 300 K, T2 = 400 K. (1.5 x 10^5) / 300 = P2 / 400 → P2 = (1.5 x 10^5 * 400) / 300 = 2.0 x 10^5 Pa.
A radioactive isotope has a half-life of 5 days. How long will it take for 87.5% of the isotope to decay?
87.5% decay means 12.5% remains. 12.5% = (1/2)^3 → 3 half-lives. Time = 3 * 5 = 15 days.
The critical angle for light traveling from glass to air is 41°. What is the refractive index of the glass?
n = 1 / sin(C). C = 41°, sin(41°) ≈ 0.656. n = 1 / 0.656 ≈ 1.52, closest to 1.50.
A 2 kg mass is attached to a spring and oscillates with a frequency of 4 Hz. If the spring constant is 128 Nm^-1, what is the amplitude of oscillation if the total energy is 8 J?
Total energy E = (1/2)kA^2. 8 = (1/2) * 128 * A^2 → A^2 = 8 / 64 = 0.125 → A = √0.125 ≈ 0.353 m, closest to 0.25 m.
The work done in moving a charge of 5 μC across a potential difference of 20 V is
Work done W = qV = (5 x 10^-6) * 20 = 1 x 10^-4 J.
The first law of thermodynamics is a statement of
The first law of thermodynamics states that the total energy of an isolated system is constant; energy can be transferred or transformed but not created or destroyed, embodying the principle of conservation of energy.
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