A body moves in a circular path of radius 10 m with a uniform speed of 5 ms^-1. What is its centripetal acceleration?
Centripetal acceleration a = v^2 / r = 5^2 / 10 = 25 / 10 = 2.5 ms^-2.
A ball of mass 0.5 kg is thrown vertically upwards with a speed of 12 ms^-1. What is its potential energy at the maximum height? (g = 10 ms^-2)
At max height, PE = initial KE = (1/2)mv^2 = (1/2) * 0.5 * 12^2 = 36 J.
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 ≈ 0.353 m, closest to 0.2 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 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 = 900 / effort → effort = 900 / 4.5 = 200 N.
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 = ρ_air * V * g = 1.2 * 2 * 10 = 24 N.
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?
P1/T1 = P2/T2. T1 = 300 K, T2 = 400 K. (1.5 x 10^5) / 300 = P2 / 400 → P2 = 2.0 x 10^5 Pa.
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?
V = (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 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 = heat gained. 0.3 * 450 * (500 - T) = 1 * 4200 * (T - 20) → 135(500 - T) = 4200(T - 20) → T ≈ 25°C.
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 = A * 2πf = 0.02 * (2π * 50) ≈ 3.14 ms^-1.
The fundamental frequency of a closed pipe is 200 Hz. If the speed of sound is 340 ms^-1, what is the length of the pipe?
f = v / (4L). 200 = 340 / (4L) → L = 340 / (200 * 4) = 0.425 m ≈ 0.43 m.
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?
f_1 = v / (2L) = 400 / (2 * 0.8) = 250 Hz. Third harmonic f_3 = 3 * 250 = 375 Hz.
The critical angle for light traveling from glass to air is 41°. What is the refractive index of the glass?
n = 1 / sin(41°) ≈ 1 / 0.656 ≈ 1.52, closest to 1.50.
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 = -1/30 → v = -30 cm (virtual, upright).
A microscope has an objective lens of focal length 2 cm and an eyepiece of focal length 5 cm. If the distance between the lenses is 18 cm, what is the magnification?
Objective: 1/2 = 1/u_o + 1/13 → u_o ≈ 2.6 cm, v_o ≈ 13 cm, m_o = 13 / 2.6 = 5. Eyepiece: m_e = 25 / 5 = 5. Total M = 5 * 5 = 25.
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 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 = 12 / 6 = 2.0 A.
A 500 W appliance operates at 250 V. How much energy does it consume in 2 hours?
Energy = 500 * 2 = 1000 Wh = 1.0 kWh.
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 = 60.
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 → 12.5% remains = (1/2)^3 → 3 half-lives = 3 * 5 = 15 days.
Which of the following particles is emitted during alpha decay?
Alpha decay emits a helium nucleus (2 protons, 2 neutrons).
The threshold frequency of a metal is 5 x 10^14 Hz. What is its work function? (h = 6.63 x 10^-34 Js)
Work function = hf = (6.63 x 10^-34) * (5 x 10^14) = 3.315 x 10^-19 J.
A particle moving at 2 x 10^6 ms^-1 has a de Broglie wavelength of 3.315 x 10^-11 m. What is its mass? (h = 6.63 x 10^-34 Js)
m = h / (λv) = (6.63 x 10^-34) / (3.315 x 10^-11 * 2 x 10^6) = 1.0 x 10^-30 kg.
Which of the following is a characteristic of gamma rays?
Gamma rays are electromagnetic waves with high penetrating power.
A car of mass 1000 kg accelerates from rest to 20 ms^-1 in 5 seconds. What is the average power developed by the engine?
Work = ΔKE = (1/2)mv^2 = (1/2) * 1000 * 20^2 = 200,000 J. Power = work / time = 200,000 / 5 = 48,000 W = 48 kW.
A projectile is launched at 30° with a speed of 20 ms^-1. What is the maximum height reached? (g = 10 ms^-2)
Vertical velocity = 20 * sin(30°) = 10 ms^-1. Max height = v^2 / (2g) = 10^2 / (2 * 10) = 5 m.
A 2 m long wire with a cross-sectional area of 1 x 10^-6 m^2 has a resistance of 8 Ω. What is the resistivity of the material?
R = ρL / A → ρ = RA / L = (8 * 1 x 10^-6) / 2 = 1.6 x 10^-5 Ωm.
A sound wave has a frequency of 500 Hz and a wavelength of 0.68 m. What is the speed of the sound wave?
v = fλ = 500 * 0.68 = 340 ms^-1.
A convex mirror has a radius of curvature of 20 cm. What is its focal length?
f = R / 2 = 20 / 2 = 10 cm.
A 6 V battery is connected to two resistors of 4 Ω and 2 Ω in series. What is the potential difference across the 4 Ω resistor?
Total resistance = 4 + 2 = 6 Ω. Current = 6 / 6 = 1 A. Voltage across 4 Ω = 1 * 4 = 4 V.
A body of mass 5 kg falls freely from a height of 10 m. What is its kinetic energy just before it hits the ground? (g = 10 ms^-2)
PE at top = mgh = 5 * 10 * 10 = 500 J. KE at ground = 500 J.
A wave travels through a medium with a speed of 200 ms^-1 and has a wavelength of 0.4 m. What is its frequency?
f = v / λ = 200 / 0.4 = 500 Hz.
A charge of 2 C experiences a force of 40 N in an electric field. What is the electric field strength?
E = F / q = 40 / 2 = 20 NC^-1.
A capacitor of 10 µF is charged to a potential difference of 100 V. What is the energy stored in the capacitor?
Energy = (1/2)CV^2 = (1/2) * (10 x 10^-6) * 100^2 = 0.05 J.
A light ray strikes a plane mirror at an angle of incidence of 30°. What is the angle of reflection?
Angle of reflection equals angle of incidence = 30°.
A 200 g object is attached to a spring with a spring constant of 50 Nm^-1. What is the period of oscillation?
T = 2π√(m/k) = 2π√(0.2/50) = 2π√(0.004) ≈ 0.8 s.
A rocket of mass 500 kg is launched with an acceleration of 20 ms^-2. What is the thrust force of the rocket? (g = 10 ms^-2)
Net force = ma = 500 * 20 = 10,000 N. Thrust = net force + weight = 10,000 + (500 * 10) = 15,000 N.
A 2 kg block slides down a frictionless incline at 30° to the horizontal. What is its acceleration down the incline? (g = 10 ms^-2)
Acceleration = g * sin(30°) = 10 * 0.5 = 5.0 ms^-2.
A parallel plate capacitor has a capacitance of 5 µF and a plate separation of 2 mm. If the separation is doubled, what is the new capacitance?
C ∝ 1/d. Doubling d halves C: 5 / 2 = 2.5 µF.
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