Science Fundamentals: Physics, Chemistry & Biology

Pressure is defined as force per unit area. The formula P = F/A is the standard equation for pressure, where P is pressure, F is force, and A is the area over which the force is distributed. The SI unit is Pascal (Pa).

Angular speed (ω) is calculated as linear speed (v) divided by radius (r), giving ω = v/r. The formula relates the tangential velocity of a point on a rotating object to its distance from the center. Option A shows this relationship.

Torque is the rotational equivalent of force, calculated as the product of force and the perpendicular distance from the pivot point (lever arm). Options A and C resemble kinetic energy formulas (½mv²), not torque equations.

Einstein's mass-energy equivalence equation is E = mc², relating energy to mass times the speed of light squared. Option B shows Planck's equation (E = hν for photon energy), and option C is the total mechanical energy formula.

Kinetic energy is the energy of motion, calculated as K = ½mv² (half mass times velocity squared). Option A (mgh) is gravitational potential energy, option C is total mechanical energy, and option D is nonsensical.

Wave speed is calculated as the product of frequency and wavelength: v = fλ. Option D correctly shows this relationship where the symbol represents wavelength. Options A and C incorrectly divide by wavelength, and option B has the correct factors but unclear notation.

The de Broglie wavelength is given by λ = h/p, where h is Planck's constant and p is momentum (p = mv). Option C correctly states this fundamental relationship in quantum mechanics.

The ideal gas law relates pressure (P), volume (V), amount of gas in moles (n), the universal gas constant (R), and temperature (T). PV = nRT is the correct and complete form.

The specific heat ratio (γ or kappa) is the ratio of specific heat at constant pressure (Cp) to specific heat at constant volume (Cv). It's a crucial parameter in thermodynamics and fluid mechanics.

According to Newton's second law of motion, force equals mass times acceleration (F = ma). This is a fundamental relationship in classical mechanics that describes how forces cause objects to accelerate.

Work is defined as the product of force and displacement in the direction of the force (W = F·d·cosθ). For force and displacement in the same direction, this simplifies to W = Fd.

The resistance of a conductor is given by R = ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area. Longer conductors have more resistance, thicker ones have less.

Ohm's law states that voltage across a conductor is directly proportional to the current flowing through it. The correct relationship is V = IR, where V is voltage, I is current, and R is resistance. Option A incorrectly omits the division operation (should be I = V/R), option B is a power formula, and option D also omits division (should be R = V/I).

When atoms from two or more different elements chemically bond together, they form a compound. Compounds have properties different from the elements that make them up. A crystal is a structured arrangement of particles, not specifically different substances joining. Particles and liquid are general terms not specific to chemical combination.

The nucleus serves as the cell's command center, housing DNA that regulates all cellular activities. Mitochondria generate energy, cytoplasm provides a medium for cellular processes, and the Golgi apparatus packages proteins. Only the nucleus contains the genetic instructions for controlling cell functions.

When breathing out, the body does not extract all oxygen from inhaled air. About 16% oxygen remains in exhaled air since humans only absorb about 4-5% of the oxygen they inhale. The options seem confused - if this meant 77% of original oxygen (21% in air), that would be about 16% remaining.

Lactose is the sugar naturally found in milk and dairy products. Glucose is blood sugar, sucrose is table sugar from plants, and fructose is fruit sugar. Lactose is unique to milk as the primary carbohydrate.

The Big Bang Theory states the universe began from a single extremely dense and hot point that expanded rapidly. The Steady-State Theory suggests continuous creation of matter. The other options are not recognized scientific theories of cosmic origin.

Pure water freezes at 32°F (0°C) at standard atmospheric pressure. This is the freezing point where liquid water transitions to solid ice. The other temperatures are incorrect for water's freezing point.

Water boils at 212°F (100°C) at sea level under standard atmospheric pressure. This is the temperature where liquid water transitions to water vapor. The other temperatures are incorrect for water's boiling point at sea level.