Thermodynamic efficiency η = Work output/Heat input = W/Q_in = 15J/60J = 0.25 = 25%. Alternatively, efficiency = 1 - Q_cold/Q_hot = 1 - 45/60 = 1 - 0.75 = 0.25 = 25%.

Absolute zero (0 K) corresponds to -273.15°C (approximately -273°C). At this temperature, all molecular motion theoretically ceases. The Kelvin scale starts at absolute zero: K = °C + 273.

A plane mirror ALWAYS produces a virtual image regardless of the object's distance. The virtual image is always the same size as the object, upright, and located as far behind the mirror as the object is in front.

Object distance u = 10cm, f = 20cm. Object is inside focal length (u < f). When object is closer than focal length, a convex lens produces a virtual, upright, and magnified (enlarged) image on the same side as the object.

Single-slit diffraction produces a central bright maximum that is wide and intense, flanked by progressively smaller and dimmer secondary maxima separated by dark minima. The central band is twice as wide as the side bands.

Refractive index n = c/v = (3×10⁸)/(2×10⁸) = 1.5. The refractive index is the ratio of the speed of light in vacuum (3×10⁸ m/s) to the speed in the medium (2×10⁸ m/s).

The electromagnetic spectrum from longest to shortest wavelength: Radio → Microwave → Infrared → Visible → Ultraviolet → X-ray → Gamma ray. So among these three: Visible light (400-700nm) > Ultraviolet (10-400nm) > X-ray (0.01-10nm).

Magnetic force F = qv×B. A stationary charge (I) experiences no magnetic force. A charge moving parallel to field (III) has v×B = 0, so no force. Only a charge moving perpendicular to B (II) experiences maximum magnetic force.

Frequency f = 4 waves/2 seconds = 2 Hz. Wave speed v = fλ = 2×0.5 = 1.0 m/s. The relationship between wave speed, frequency, and wavelength is v = fλ.

Wave speed v = √(T/μ) where T is tension and μ is mass per unit length. Greater tension → greater wave speed. Frequency remains constant when a wave passes between media (determined by the source). So the speed increases.

In a step-down transformer, voltage is decreased and current is increased. Power and frequency remain constant (ideal transformer). V1I1 = V2I2 — as voltage steps down, current steps up proportionally.

Electric potential V = W/q (work done per unit charge to move a positive test charge from reference to a point). It is a scalar quantity (not vector). It is measured in volts (J/C), not N/C (which is the electric field unit).

When connected by a wire, total charge redistributes equally: Q_total = -3+1 = -2C. Each sphere gets -2C/2 = -1C. The charge distributes equally between two identical conducting spheres.

For a planet in orbit, angular momentum L = mvr is conserved (no external torque). Velocity and radius vary (elliptical orbits — Kepler's 2nd law). Gravitational force varies with distance (F = GMm/r²).

For a simple pendulum, the period T = 2π√(L/g) is independent of amplitude (for small angles). Increasing amplitude does NOT change the period or frequency. This is the isochronous property of the pendulum.

Conservation of angular momentum: L = mvr = constant. When r becomes r/2: m×v'×(r/2) = mvr → v' = 2v. As the radius halves, the speed doubles to conserve angular momentum.

By the law of conservation of mechanical energy (neglecting air resistance), the total mechanical energy (KE + PE) remains constant throughout the fall. As PE decreases, KE increases by exactly the same amount.

Work is NOT a vector — it is a scalar quantity (the dot product of two vectors is a scalar). W = F.d.cosθ has magnitude only, no direction. All other statements about work are true.

By conservation of momentum: total initial momentum = 0 (system at rest). Therefore, momentum of cannon = -(momentum of cannonball). Their magnitudes are equal. The velocities are not equal (they differ by mass ratio).

For the block to remain at rest, friction equals the component of gravity along the plane. F_friction = mg×sin30° = 2×10×0.5 = 10N. This balances the gravitational component pulling the block down the slope.

Newton's 3rd Law: Action-reaction pairs act on different objects. Earth pulls ball down (action) → ball pulls earth up (reaction). These forces are equal in magnitude but opposite in direction, forming an action-reaction pair.

By symmetry, the vertical component of velocity just before landing equals the initial vertical component (same magnitude). Initial vertical component = v×sin30° = 40×0.5 = 20 m/s. The final vertical speed is also 20 m/s (downward).

Statement B is false — the vertical velocity is upward from launch until maximum height (not first half of time), then downward. For asymmetric launches, the halfway point in time does not correspond to halfway in vertical velocity direction.

These vectors are perpendicular (east and north), so the resultant = √(3² + 4²) = √(9+16) = √25 = 5m. The direction is northeast (between east and north). This is a classic 3-4-5 right triangle.

Mass is a scalar quantity — it has magnitude only (e.g., 5 kg) with no direction. Displacement, resultant, and equilibrant are all vector quantities that have both magnitude and direction.