Which of the following is a vector quantity?
Velocity is a vector with magnitude and direction, unlike temperature, speed, and energy, which are scalars.
A stone is dropped from a height of 45 m. How long does it take to reach the ground? (g = 10 ms^-2)
Using s = ut + (1/2)gt^2, u = 0, s = 45 m, g = 10 ms^-2: 45 = 5t^2 → t^2 = 9 → t = 3 s.
A force of 10 N acts on a 2 kg body for 4 s. What is the change in momentum?
Change in momentum = force × time = 10 × 4 = 40 kgms^-1.
A projectile is launched at 30° with a velocity of 20 ms^-1. What is the horizontal component of its velocity?
Horizontal component = v × cos(30°) = 20 × (√3/2) ≈ 17.3 ms^-1.
A 5 kg body moves at 8 ms^-1. What is its kinetic energy?
Kinetic energy = (1/2)mv^2 = (1/2) × 5 × 64 = 320 J.
A pulley system lifts a 600 N load with a 200 N effort. What is the mechanical advantage?
Mechanical advantage = load / effort = 600 / 200 = 3.
A helium-filled balloon rises because
Helium’s lower density than air creates buoyancy, causing the balloon to rise.
A liquid exerts 5000 Pa at a depth of 2 m. What is its density? (g = 10 ms^-2)
P = ρgh. 5000 = ρ × 10 × 2 → ρ = 5000 / 20 = 250 kgm^-3.
A gas is compressed to half its volume at constant temperature. What happens to its pressure?
At constant temperature, P1V1 = P2V2 (Boyle’s law). If V2 = V1/2, P2 = P1 × 2, so pressure doubles.
A metal cube of side 0.1 m is heated from 20°C to 220°C. If its linear expansivity is 2 × 10^-5 K^-1, what is the volume increase?
γ = 3α = 3 × 2 × 10^-5 = 6 × 10^-5 K^-1. V = (0.1)^3 = 0.001 m^3. ΔV = V × γ × ΔT = 0.001 × 6 × 10^-5 × 200 = 3.6 × 10^-4 m^3.
What is the specific heat capacity if 1500 J raises 0.5 kg of a substance by 5°C?
Q = mcΔT. c = Q / (mΔT) = 1500 / (0.5 × 5) = 600 Jkg^-1K^-1.
The boiling point of water decreases when
Lower pressure reduces the energy needed for boiling, decreasing the boiling point.
A wave travels at 300 ms^-1 with a frequency of 600 Hz. What is its wavelength?
λ = v / f = 300 / 600 = 0.5 m.
The speed of sound in air at 20°C is 343 ms^-1. What is it at 40°C?
v ∝ √T. v2/v1 = √(313/293) ≈ 1.034. v2 = 343 × 1.034 ≈ 355 ms^-1.
A pipe closed at one end has a fundamental frequency of 170 Hz. If the speed of sound is 340 ms^-1, what is the pipe’s length?
f = v / (4L). 170 = 340 / (4L) → 4L = 2 → L = 0.50 m.
Which phenomenon demonstrates the particle nature of light?
The photoelectric effect shows light as photons ejecting electrons.
An object is 20 cm from a concave mirror with a 15 cm focal length. What is the nature of the image?
1/f = 1/u + 1/v. 1/15 = 1/20 + 1/v → 1/v = 1/60 → v = 60 cm (real). Beyond focal point, image is real and inverted.
A glass prism (n = 1.5) has a 60° apex angle. What is the angle of minimum deviation?
δ_m = (n - 1)A = (1.5 - 1) × 60 = 30°.
A charged particle (q = 2 × 10^-6 C, v = 5 ms^-1) moves at 60° to a magnetic field, experiencing a 3 × 10^-3 N force. What is the field strength?
F = qvB sin(60°). B = F / (qv × 0.866) = (3 × 10^-3) / (2 × 10^-6 × 5 × 0.866) ≈ 0.4 T.
A wire with 2 A current in a 0.5 T field (0.1 m length, 90° angle) experiences what force?
F = BIL sin(90°) = 0.5 × 2 × 0.1 × 1 = 0.10 N.
A transformer has 200 primary and 800 secondary turns. If the primary voltage is 50 V, what is the secondary voltage?
Vs/Vp = Ns/Np. Vs/50 = 800/200 → Vs = 50 × 4 = 200 V.
A 12 V battery connects two resistors (4 Ω and 8 Ω) in series. What is the voltage across the 8 Ω resistor?
Total R = 12 Ω. I = V/R = 12/12 = 1 A. Voltage across 8 Ω = 1 × 8 = 8 V.
A household uses 10 kWh in 5 hours. What is the average power consumption?
Power = energy / time = 10 kWh / 5 h = 2 kW.
Which is NOT a property of electromagnetic waves?
Electromagnetic waves propagate through a vacuum, unlike mechanical waves.
A substance with an 8-day half-life takes how long for 75% to decay?
75% decay → 25% remains = (1/2)^2. 2 half-lives = 2 × 8 = 16 days.
Which particle has the highest penetrating power?
Gamma rays, being electromagnetic, penetrate most materials easily.
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)
φ = hc/λ = (6.63 × 10^-34 × 3 × 10^8) / (6 × 10^-7) ≈ 3.3 × 10^-19 J.
A neutron splits a uranium nucleus into two fragments in
Fission splits a heavy nucleus into smaller fragments.
A p-n junction diode conducts easily when
Forward bias reduces the barrier, allowing current flow.
A particle’s de Broglie wavelength is 2 × 10^-10 m, mass 9.1 × 10^-31 kg. What is its velocity? (h = 6.63 × 10^-34 Js)
λ = h / (mv). v = h / (mλ) = (6.63 × 10^-34) / (9.1 × 10^-31 × 2 × 10^-10) ≈ 4.0 × 10^3 ms^-1.
Which is a characteristic of X-rays?
X-rays are electromagnetic waves with high penetration, not deflected by fields.
A 2 μF capacitor is charged to 100 V. What is the stored energy?
Energy = (1/2)CV^2 = (1/2) × 2 × 10^-6 × (100)^2 = 0.02 J.
A mass of 0.5 kg oscillates with a period of 2 s. What is the spring constant? (Assume SHM)
T = 2π√(m/k). 2 = 2π√(0.5/k) → 1/π = √(0.5/k) → k = 0.5 × π^2 ≈ 4.94 Nm^-1.
Two charges of 4 μC and 9 μC are 0.3 m apart. What is the electric field strength at a point midway between them? (k = 9 × 10^9 Nm^2C^-2)
E = kq/r^2. At midpoint, r = 0.15 m. E_total = E1 + E2 = (9 × 10^9 × 4 × 10^-6 / 0.15^2) + (9 × 10^9 × 9 × 10^-6 / 0.15^2) ≈ 4.0 × 10^5 NC^-1.
A source emits sound at 500 Hz, moving at 20 ms^-1 toward a stationary observer. If the speed of sound is 340 ms^-1, what frequency is observed?
f’ = f × (v / (v - vs)) = 500 × (340 / (340 - 20)) = 500 × (340/320) ≈ 540 Hz.
A wire of length 0.5 m and cross-sectional area 2 × 10^-6 m^2 extends by 0.02 m under a 100 N force. What is Young’s modulus?
Y = (F/A) / (ΔL/L) = (100 / 2 × 10^-6) / (0.02 / 0.5) = (5 × 10^7) / 0.04 = 2.0 × 10^10 Nm^-2.
A convex lens has a focal length of 20 cm. An object is placed 30 cm from the lens. What is the image distance?
Using the lens formula 1/f = 1/u + 1/v: 1/20 = 1/30 + 1/v → 1/v = 1/20 - 1/30 = 1/60 → v = 60 cm.
A car accelerates uniformly from rest to 20 ms^-1 in 5 s. What is the acceleration?
a = (v - u) / t = (20 - 0) / 5 = 4 ms^-2.
A 1000 kg car moves at 20 ms^-1. What is the work done to bring it to rest?
Work done = initial kinetic energy = (1/2)mv^2 = (1/2) × 1000 × (20)^2 = 2 × 10^5 J.
A transverse wave has an amplitude of 0.02 m and a wavelength of 4 m. What is the maximum displacement from the equilibrium position?
Maximum displacement in a transverse wave is the amplitude, which is 0.02 m.
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