Physics: Dimensions, Errors, and Motion

Dimensional Analysis & Errors

• Planck's constant has the dimension of [ML²T⁻¹].
• Power x time, force x distance, momentum x velocity, and pressure x area, has the same dimension as does energy.
• A measurement of 9.2 ± 0.1 cm has a relative error of approximately 1.08%.
• The incorrect pair is power - [MLT⁻³]

Instruments & Derived Quantities

• A Screw gauge with LC = 0.001 cm has the most precision
• Potential energy (PE) can be Stored PE in a spring given by: kx²

Centripetal Acceleration

• Centripetal acceleration, using the vector method, is v²/r.

Non-SI Units

• Angle cannot be derived using base SI units.

Indirect Applications & Graphs

• A displacement-time parabola indicates constant acceleration.
• Same displacement-time but different velocity-time graphs signifies different accelerations.
• The graph for vertical throw upward is a parabola opening downward.
• Using a stopwatch for time is an example of indirect measurement.

Motion Under Gravity & Galileo Ratio

• The correct equation for free fall begins as s = ut + (1/2)gt².
• Time to reach max height is u/g.
• Galileo's ratio of distances in equal time is 1:3:5...
• Distance in the 3rd second of free fall is u + (1/2)g(5-4).

Vectors & Rain-Man

• The resultant of two vectors is maximum when the angle is 0°.
• Rain appears slanted when a man walks.
• The time it takes a boat to cross a river of width d can be calculated by d/v, only if perpendicular.
• Minimum crossing time occurs when going perpendicular to the stream.

Projectile Motion

• Time of flight is 2usinθ/g.
• Max height is u²sin²θ / 2g.
• The equation of trajectory is a parabola.
• When R = 80 m at 45°, the maximum height is 20 m.

Hmax and Rmax

• When the angle is 45°, the relation is R = 4H.
• H/R = 1/4.

Friction & Incline

• Two blocks on an incline with friction has an acceleration formula of a = g sin θ.
• No slipping condition is μ > tan θ.
• Net force on a sliding block is mg(sin θ - μcos θ).

Circular Motion & Pseudo Force

• Friction for circular turn is mv²/r.
• Pseudo force appears in non-inertial frames.

Connected Motion

• Acceleration of 2 masses over a pulley is (m1-m2)g/(m1+m2).
• Tension in a string (horizontal) is T = ma.

Work, Energy, Power

• Work by a conservative force is path independent.
• Mechanical energy gained is mgh.
• A 100W bulb used for 1 hour consumes 360 kJ of energy.

Collision & VCM

• Elastic collision conserves both momentum and kinetic energy.
• VCM for masses m1 and m2 is (m1v1+m2v2)/(m1+m2).

Potential Energy

• Spring PE vs x graph is a parabola.
• Simple Harmonic Motion PE is minimum at the mean position.

Logic Gates

• An AND gate gives 1 when both inputs are 1.
• A NOT gate output for input 1 is 0.
• An XOR gate gives 1 when inputs are different.
• An OR gate truth table shows 1 when one input is 1.

Basic Concepts of Organic Chemistry

• CH3CH2CH2OH is named Propanol.
• A position isomer of butanol is Butan-2-ol.
• -CH3 group shows a +I effect.
• -NO2 group shows a -M effect.
• SN1 reactions are favored in polar protic solvents.
• In SN2 reactions, inversion of configuration occurs.
• The presence of phenol is confirmed by FeCl3 solution during a chemical test.
• Lucas reagent distinguishes between primary, secondary, and tertiary alcohols.
• A compound giving a white precipitate with AgNO3 likely contains alkyl halide.
• C6H5OH does not give effervescence with NaHCO3.

Mole Concept & Stoichiometry

• 22.4 L of CO2 at STP is 1 mole.
• Two moles of water contain 1.204×10²⁴ molecules.
• In a reaction of 5g of H2 with 160g of O2, O2 is the limiting reagent.
• If a reaction yields 90g of product from a theoretical 100g, the percentage yield is 90%.
• 200 mL of 0.5 M NaOH is required to neutralize 100 mL of 1 M HCl.

Avogadro's Number and Empirical Formula

• Avogadro's number is 6.022×10²³.
• The empirical formula of a compound with C: 75%, H: 25% is CH3.

Atomic Structure & Quantum Mechanics

• According to Bohr's model, angular momentum is quantized as nh/2π.
• The quantum number ‘l' determines orbital shape.
• The maximum number of electrons in a subshell with l = 1 is 6.
• Heisenberg's uncertainty principle relates position and momentum.
• If Δx × Δp ≥ h/4π, the uncertainty in momentum increases if Δx is small.

Orbitals and Quantum Numbers

• The 2s orbital has the lowest energy in a multi-electron atom.
• The total number of orbitals for n = 3 is 9.
• The magnetic quantum number (m) for a d-orbital can be -2 to +2.
• The spin quantum number can have values of +½ or -½.
• The azimuthal quantum number (l) for a p-orbital is 1.
• The number of nodes in a 3s orbital is 2.

Periodic Properties

• Atomic radius decreases across a period.
• Iodine, (I) has the largest atomic size.
• Ionization enthalpy is lowest for Potassium (K).
• Electron gain enthalpy is highest for Chlorine (Cl).
• Lead (Pb) shows the inert pair effect.
• Fluorine and Chlorine (F and Cl) have the same number of valence electrons.
• Fluorine has the highest electronegativity.

Chemical Bonding & Properties

• The bond order in O2 is 2.
• Chlorine has the highest bond length.
• BF3 has sp² hybridization.
• Carbon dioxide is a linear molecule
• Oxygen is paramagnetic.
• The bond angle in CH4 is approximately 109.5°.
• Carbon monoxide is a neutral oxide.
• Al2O3 is an amphoteric oxide.
• BF3 has sp² hybridization.
• CH4 exhibits sp³ hybridization.
• Molecular orbital configuration of O2 shows unpaired electrons in π*2p.

Cell Biology

• Ribosomes are a feature of prokaryotic cells.
• Mitochondria are responsible for the synthesis of ATP.
• Modification, sorting, and packaging proteins is the primary function of the Golgi apparatus.
• The function of chloroplasts is photosynthesis.
• Cellulose is the main constituent of the plant cell wall.
• The breakdown of cellular waste and toxins is performed by Lysosome.
• Site of photosynthesis is not a characteristic of mitochondria.
• Ribosomes are found in both plant and animal cells.
• Ribosomes are the site of protein synthesis.
• The smooth endoplasmic reticulum (SER) is involved in lipid synthesis.
• The plasma membrane regulates the passage of materials into and out of the cell.
• Endocytosis involves the engulfment of large particles by the cell.
• The nucleolus is responsible for the synthesis of ribosomal RNA (rRNA).
• The Golgi apparatus is responsible for protein modification and packaging.
• Cytoskeleton's function is in maintaining cell shape and structure.
• Ribosomal RNA (rRNA) is the most abundant type of RNA in a cell.
• Organisms that produce their own food through photosynthesis or chemosynthesis and are autotrophic.
• Hormones are responsible for cellular communication in multicellular organism.

Microbes

• Influenza A diseases causes a viral disease.
• Viruses do not reproduce independently.
• The process of nitrogen fixation is carried out by nitrogen-fixing bacteria.
• Malaria is caused by a protozoan.
• Denitrification, Nitrogen fixation, and Ammonification are functions of bacteria in the nitrogen cycle.
• DNA, present in the cytoplasm, is the genetic material of most bacteria.
• Airborne transmission is the most common mode of transmission of viral infections.
• Conjugation in bacteria involves the exchange of DNA between two bacteria.
• Fungi can be multicellular or unicellular.
• Plasmids carry additional genes, often responsible for antibiotic resistance in bacteria.
• The capsule in bacteria helps to protect the cells from phagocytosis.
• Mycobacterium tuberculosis is responsible for causing tuberculosis.
• A role of viruses : Regulate populations of microorganisms.
• Retrovirus : A characteristic feature of the HIV virus.
• Bacterial spores let bacteria survive in unfavorable conditions.
• Nitrogen fixation is a Conversion of nitrogen gas into ammonia.
• The vector Anopheles mosquito transmits malaria.
• Viruses are an example of obligate intracellular parasites.
• Controlling microbial growth : Freezing.

Living World

• Autotroph/Heterotroph classification, cellular level organization, and ability to reproduce are all characteristics of living organisms.
• Carl Linnaeus is the father of modern taxonomy.
• The binomial nomenclature system : is based on which using two names (genus and species). In the hierarchical classification system, the taxonomic rank that is below kingdom is Phylum.
• Amoeba is classify under the kingdom Protista.
• A three-domain system includes Bacteria, Archaea, Eukarya
• The kingdom Fungi includes Yeasts, molds, mushrooms.
• Plants is a producer in an ecosystem?
• The classification of organisms based on shared evolutionary traits is called Phylogenetic classification.
• Animalia contains Multicellular, eukaryotic organisms.

Body Fluids

• Hemoglobin is a component, found in blood plasma, not in blood cells.
• The function of red blood cells, is to carry the oxygen to tissues.
• Blood type O is known as the universal donor.
• The main role of platelets is to help in blood clotting.
• The liquid portion of blood responsible for transporting nutrients, waste, and gases is called plasma.
• Leukocytes are the blood cells involved in immune response.
• Lymph does immune response and fluid balance.
• The clotting process includes Fibrinogen
• Human blood has an average pH of 7.4.
• The hormone Erythropoietin aids in the production of red-blood cells.
• Lymphatic system helps in Immunity and fluid balance.
• Blood clotting is associated with Fibrinogen.
• The Rh factor in blood helps with Blood type incompatibility.
• Plasma has contains contains no proteins.

Evolution

• Natural selection's concept was proposed by Charles Darwin.
• Evidence for evolution is not found in Individuals that changing their traits within a lifetime.
• When one species evolves into several different forms to adapt to different environments this is called divergent evolution
• Convergent evolution occurs when unrelated species develop similar characteristics due to similar environmental pressures.
• It fossil record indicate The changes in species over time.
• Examples of natural selection:
• The breeding of dogs with specific traits are artificial selection.
• In Hardy-Weinberg, alleles of a population : There must be no mutation. Large population. Random mating
• Genetic Drift. : the more pronounced in small populations.
• Examples human appendix: vestigial structures
• The concept of survival of the flittest is most closely associated: Natural selection. Examples of evolution of convergent of wings in birds and bats.
• Jean Batist Lamrack: Contributed.
• Ways does genetic variation occur: Alleles is involved.
• A feature a characteristics of a living animal: Fossil and living species Moth during the industrial period, not a adaptation. The wing of a human and animal Part the human body: Wings in birds and bats.
• Genetic variation occur in Mutations.

Cellular Components and Functions

• The a part of the endomembrane system ; The Endoplasmatic reticulum.
• The true about mitochondria? Their contains DNA.
• Tuberculosis is : The causative agent.
• Antibiotics has effective against Bacteria.

Prokaryotes

• Lack of membrane-bound is the feature of prokaryotes. -A Sequence of taxonomic ranks
• Kingdom.
• The
• Red blood cell Is responsible for the production of.
• Plasma proteins is related: Osmotic balance.
• Bat and Human.