Kochi Entrance Science flashcards

35 cards. Read the term and the definition here. The deck at the top of this page is optional.

Newton's second law

The net force on a body equals its mass times acceleration, ΣF = ma. Apply it separately along each chosen axis, and radially for circular motion as mv²/r.

Conservation of momentum

With no net external impulse, total momentum before an event equals total momentum after, as in collisions and explosions. Kinetic energy is conserved only in elastic collisions.

Simple harmonic motion condition

Acceleration is proportional to displacement and directed opposite to it, a = −ω²x. The period is 2π√(m/k) for a spring and 2π√(l/g) for a small-angle pendulum.

Projectile motion components

Horizontal velocity stays constant while vertical motion has constant acceleration g. On level ground the time of flight is 2u sinθ/g and range is u² sin2θ/g.

Wave speed relation

Speed equals frequency times wavelength, v = fλ. When a wave enters a new medium the frequency stays fixed and speed and wavelength change together.

Standing wave on string

A string fixed at both ends supports wavelengths λ = 2L/n and frequencies f = nv/(2L). A pipe closed at one end supports odd harmonics only.

Total internal reflection

Occurs only when light travels from a denser to a rarer medium and the angle of incidence exceeds the critical angle, where sinθ_c = n₂/n₁.

Doppler effect for sound

Observed frequency rises when source and observer approach and falls when they separate. The shift depends on the speeds of both source and observer relative to the wave speed.

Resistors in parallel

Parallel resistors share the same voltage and their reciprocals add: 1/R_total = 1/R₁ + 1/R₂ + … The combined resistance is always less than the smallest individual resistance.

Faraday's law of induction

Induced emf equals the negative rate of change of magnetic flux, −dΦ/dt, where Φ = BA cosθ. Lenz's law makes the induced current oppose the flux change.

Energy stored in a capacitor

A charged capacitor stores energy ½CV², equivalently ½QV or Q²/2C. Capacitors in parallel add directly; in series their reciprocals add.

Kirchhoff's circuit rules

The junction rule states current into a junction equals current out, expressing charge conservation. The loop rule states the sum of potential differences around any closed loop is zero.

VSEPR bond angles

Electron pairs repel to maximum separation, and lone pairs repel more strongly than bonding pairs. Methane is 109.5°, ammonia 107° and water 104.5°.

Hydrogen bonding

A strong dipole attraction between hydrogen bonded to N, O or F and a lone pair on a nearby N, O or F atom. It raises boiling points, as in water and hydrogen fluoride.

Electronegativity and molecular polarity

A bond is polar when electronegativity differs. The molecule is polar only if polar bonds are arranged asymmetrically, so carbon dioxide is non-polar but water is polar.

Hybridisation and geometry

sp hybridisation gives linear geometry with 180° angles, sp² gives trigonal planar 120°, and sp³ gives tetrahedral 109.5°. Count electron domains to assign the type.

Le Chatelier's principle

When a system at equilibrium is disturbed, it shifts in the direction that opposes the change. Raising pressure favours fewer gas moles; raising temperature favours the endothermic direction.

Reaction quotient versus K

Q has the equilibrium expression form but uses current concentrations. If Q < K the forward reaction is favoured, if Q > K the reverse, and if Q = K the system is at equilibrium.

Limiting reagent

The reactant that runs out first, found by dividing moles of each reactant by its coefficient and taking the smallest value. It determines the maximum theoretical product yield.

pH of strong and weak acids

pH = −log[H⁺]. A strong monoprotic acid of concentration c gives pH = −log c, while a weak acid needs Ka and an equilibrium calculation because it only partly dissociates.

Mitosis versus meiosis

Mitosis yields two identical diploid cells for growth and repair. Meiosis yields four genetically varied haploid gametes through crossing over and independent assortment of chromosomes.

Complementary base pairing

In DNA, adenine pairs with thymine and guanine with cytosine through hydrogen bonds. In RNA, adenine pairs with uracil instead of thymine during transcription and translation.

Monohybrid cross ratio

Crossing two heterozygotes gives a 3:1 phenotypic ratio and a 1:2:1 genotypic ratio. A test cross with the recessive phenotype reveals an unknown dominant genotype.

Transcription and translation

Transcription copies DNA into messenger RNA in the nucleus. Translation at the ribosome reads each codon and adds the matching amino acid to build a polypeptide chain.

Insulin and glucagon

Insulin lowers blood glucose by promoting cellular uptake and glycogen formation. Glucagon raises it by stimulating glycogen breakdown in the liver, giving negative feedback control.

Alveolar gas exchange

Alveoli provide a large, thin, moist surface with a steep concentration gradient, so oxygen diffuses into blood and carbon dioxide diffuses out. Ventilation maintains the gradient.

Energy transfer in food chains

Only about ten percent of energy passes to the next trophic level, the rest lost through respiration, heat and excretion. This makes energy pyramids steep and limits chain length.

Logistic population growth

Population growth slows as size approaches the carrying capacity K set by limited resources. The curve is S-shaped, unlike unlimited exponential J-shaped growth.

Quadratic discriminant

For ax² + bx + c = 0, the discriminant b² − 4ac determines root type: positive gives two distinct real roots, zero gives one repeated root, negative gives complex roots.

Sum and product of roots

For ax² + bx + c = 0 with roots α and β, the sum α + β equals −b/a and the product αβ equals c/a. These allow equations to be built from known roots.

Remainder and factor theorems

Dividing polynomial P(x) by (x − a) leaves remainder P(a). The divisor is a factor exactly when P(a) = 0, which allows factorising and finding roots.

Geometric series sum

For first term a and ratio r, the nth term is arⁿ⁻¹ and the sum is a(1 − rⁿ)/(1 − r) for r ≠ 1. An infinite series converges only when |r| < 1.

Chain rule

For a composite function, dy/dx = dy/du × du/dx. It differentiates nested functions such as (3x + 1)⁵ or sin(x²) by working through the inner variable.

Second derivative test

At a stationary point where f'(x) = 0, f''(x) > 0 indicates a local minimum and f''(x) < 0 a local maximum. If f''(x) = 0 further testing is needed.

Perpendicular line gradients

Two lines are perpendicular when the product of their gradients equals −1, so one gradient is the negative reciprocal of the other. Parallel lines have equal gradients.