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Density is mass per unit volume, found by dividing mass by volume."},{"text":"mass multiplied by volume","correct":false,"explanation":"Multiplying mass by volume does not describe how concentrated the matter is. Density is mass divided by volume, or mass per unit volume."},{"text":"volume divided by mass","correct":false,"explanation":"Dividing volume by mass gives the reciprocal of density. The correct definition is mass per unit volume, because density compares mass with the space it occupies."}]},{"id":"04e76122-ad05-49bd-9872-2f823a9fbae3","cardType":"cloze","points":null,"front":"Density is mass per unit volume and has the symbol $\\text{[...]}$.","back":"Density is mass per unit volume and has the symbol $\\boxed{\\rho}$.","mcqOptions":[{"text":"$$\\rho$","correct":true,"explanation":"The Greek letter rho, $\\rho$, is the standard symbol used for density in the density equation and in physics notation."},{"text":"$$\\mu$","correct":false,"explanation":"The Greek letter mu is commonly used for coefficients of friction or prefixes, not density. Density is represented by rho, $\\rho$."},{"text":"$$\\sigma$","correct":false,"explanation":"Sigma is used for quantities such as stress or summation in different contexts, but it is not the standard density symbol. Density uses rho, $\\rho$."},{"text":"$$\\delta$","correct":false,"explanation":"Delta can represent a change in a quantity, but it is not the conventional symbol for density. The accepted symbol for density is rho, $\\rho$."}]},{"id":"77e2af70-df1f-4ab2-94cd-963ba75bbc66","cardType":"basic","points":1,"front":"Two objects have the same volume. Which has greater density?","back":"The object with the greater mass.","mcqOptions":[{"text":"The object with the greater mass.","correct":true,"explanation":"With equal volumes, density increases as mass increases because density equals mass divided by volume. Therefore, the object with greater mass is denser."},{"text":"The object with the smaller mass.","correct":false,"explanation":"This reverses the mass relationship. When volume is the same, the greater mass gives the greater density because density is mass divided by volume."},{"text":"The object with the greater volume.","correct":false,"explanation":"The volumes are already equal, so volume cannot distinguish the densities. With equal volume, the object with greater mass has greater density."},{"text":"Both objects have the same density.","correct":false,"explanation":"Equal volume alone does not guarantee equal density. If the masses differ, the greater mass produces the greater density using $\\rho = \\dfrac{m}{V}$."}]},{"id":"037ee78f-29aa-4439-a5e7-e9fb35ec712e","cardType":"basic","points":1,"front":"Two objects have the same mass. Which has greater density?","back":"The object with the smaller volume.","mcqOptions":[{"text":"The object with the smaller volume.","correct":true,"explanation":"With equal masses, density is greater when the same mass occupies less space. Dividing the fixed mass by a smaller volume gives a larger density."},{"text":"The object with the greater volume.","correct":false,"explanation":"A greater volume spreads the same mass over more space, reducing density. With equal masses, the smaller-volume object is denser."},{"text":"The object with the smaller mass.","correct":false,"explanation":"The masses are equal, so mass cannot distinguish the objects. The smaller volume gives greater density because density is mass divided by volume."},{"text":"Both objects have the same density.","correct":false,"explanation":"Equal mass does not mean equal density when volumes differ. The object with smaller volume has greater density because its mass is more concentrated."}]},{"id":"7e1bfb1e-b7db-481b-bc58-f4b8c211b986","cardType":"cloze","points":null,"front":"Density is calculated using $\\text{[...]}$, so its standard unit is $\\text{kg/m}^3$.","back":"Density is calculated using $\\boxed{\\rho = \\dfrac{m}{V}}$, so its standard unit is $\\text{kg/m}^3$.","mcqOptions":[{"text":"$$\\rho = \\dfrac{m}{V}$","correct":true,"explanation":"Density is calculated by dividing mass, $m$, by volume, $V$. This relationship is written as $\\rho = \\dfrac{m}{V}$ and gives the unit $\\text{kg/m}^3$."},{"text":"$$\\rho = \\dfrac{V}{m}$","correct":false,"explanation":"This reverses the density formula and calculates volume per unit mass. Density is mass divided by volume: $\\rho = \\dfrac{m}{V}$."},{"text":"$$\\rho = mV$","correct":false,"explanation":"Multiplying mass by volume does not calculate density. Density measures mass packed into a volume, so the correct equation divides mass by volume."},{"text":"$$\\rho = m + V$","correct":false,"explanation":"Mass and volume are not added to find density, and their units would not produce $\\text{kg/m}^3$. Use $\\rho = \\dfrac{m}{V}$."}]},{"id":"e97e9d6f-a4a8-4da8-b9b9-6f5dd4c0a831","cardType":"cloze","points":null,"front":"Density is calculated using $\\rho = \\dfrac{m}{V}$, so its standard unit is $\\text{[...]}$.","back":"Density is calculated using $\\rho = \\dfrac{m}{V}$, so its standard unit is $\\boxed{\\text{kg/m}^3}$.","mcqOptions":[{"text":"$$\\text{kg/m}^3$","correct":true,"explanation":"Using mass in kilograms and volume in cubic metres gives density in kilograms per cubic metre, written $\\text{kg/m}^3$."},{"text":"$$\\text{kg/m}^2$","correct":false,"explanation":"The square metre unit measures area, not volume. Density divides mass by cubic metres, so its standard unit is $\\text{kg/m}^3$."},{"text":"$$\\text{g/cm}^3$","correct":false,"explanation":"Grams per cubic centimetre is also a valid density unit, but it is not the standard SI unit requested here. The standard unit is $\\text{kg/m}^3$."},{"text":"$$\\text{m}^3/\\text{kg}$","correct":false,"explanation":"This unit represents volume per unit mass, the reciprocal of density. Density is mass divided by volume, giving $\\text{kg/m}^3$."}]},{"id":"d862a3e5-ad14-4a73-8dba-20270419e1b7","cardType":"cloze","points":null,"front":"In the density equation, mass is measured in $\\text{[...]}$ and volume in $\\text{m}^3$.","back":"In the density equation, mass is measured in $\\boxed{\\text{kg}}$ and volume in $\\text{m}^3$.","mcqOptions":[{"text":"$$\\text{kg}$","correct":true,"explanation":"The standard density equation uses mass in kilograms and volume in cubic metres, producing density in $\\text{kg/m}^3$."},{"text":"$$\\text{g}$","correct":false,"explanation":"Grams can measure mass, but the standard SI form of the density equation uses kilograms when volume is in $\\text{m}^3$."},{"text":"$$\\text{N}$","correct":false,"explanation":"Newtons measure force, not mass. Density calculations require mass in kilograms when volume is measured in cubic metres."},{"text":"$$\\text{kg/m}^3$","correct":false,"explanation":"Kilograms per cubic metre is the unit of density, not mass. The mass term itself is measured in kilograms, $\\text{kg}$."}]},{"id":"ec4c4ead-5f48-404e-8418-1facb406631e","cardType":"cloze","points":null,"front":"In the density equation, mass is measured in $\\text{kg}$ and volume in $\\text{[...]}$.","back":"In the density equation, mass is measured in $\\text{kg}$ and volume in $\\boxed{\\text{m}^3}$.","mcqOptions":[{"text":"$$\\text{m}^3$","correct":true,"explanation":"Volume is measured in cubic metres in the standard density equation. Dividing kilograms by cubic metres produces density in $\\text{kg/m}^3$."},{"text":"$$\\text{m}^2$","correct":false,"explanation":"Square metres measure area, whereas volume requires three dimensions and is measured in cubic metres. The correct unit is $\\text{m}^3$."},{"text":"$$\\text{cm}^3$","correct":false,"explanation":"Cubic centimetres can measure volume, but the standard SI unit used with kilograms in this equation is cubic metres, $\\text{m}^3$."},{"text":"$$\\text{m}$","correct":false,"explanation":"Metres measure length, not three-dimensional volume. Volume in the density equation must be measured in cubic metres, $\\text{m}^3$."}]},{"id":"5c13471d-2574-4a92-bb77-dec9875f7e3a","cardType":"cloze","points":null,"front":"To convert from $\\text{g/cm}^3$ to $\\text{kg/m}^3$, [ ].","back":"To convert from $\\text{g/cm}^3$ to $\\text{kg/m}^3$, multiply by 1000.","mcqOptions":[{"text":"multiply by 1000","correct":true,"explanation":"The conversion from $\\text{g/cm}^3$ to $\\text{kg/m}^3$ multiplies the numerical value by 1000, accounting for both the mass and volume unit changes."},{"text":"divide by 1000","correct":false,"explanation":"Dividing by 1000 reverses the conversion direction. To change $\\text{g/cm}^3$ into $\\text{kg/m}^3$, multiply the numerical value by 1000."},{"text":"multiply by 100","correct":false,"explanation":"This misses the combined effect of converting grams to kilograms and cubic centimetres to cubic metres. The correct numerical conversion factor is 1000."},{"text":"leave the value unchanged","correct":false,"explanation":"The units are different, so the numerical value must change. A density in $\\text{g/cm}^3$ is converted to $\\text{kg/m}^3$ by multiplying by 1000."}]},{"id":"1afd654e-7d89-4ac2-937c-e4576152d828","cardType":"basic","points":2,"front":"Why does a solid keep a fixed shape?","back":"They vibrate about fixed positions and cannot move past each other.","mcqOptions":[{"text":"They vibrate about fixed positions and cannot move past each other.","correct":true,"explanation":"Particles in a solid are held in fixed positions. They can vibrate, but their strong attractions prevent them from moving past one another, giving the solid a fixed shape."},{"text":"They move freely in all directions and cannot move past each other.","correct":false,"explanation":"Particles that move freely would not maintain fixed positions or a fixed shape. Solid particles vibrate about fixed positions and cannot move past each other."},{"text":"They stay completely still and cannot move past each other.","correct":false,"explanation":"Solid particles are not motionless: they vibrate about their fixed positions. This vibration occurs without particles moving past one another."},{"text":"They move past each other and remain in fixed positions.","correct":false,"explanation":"These two descriptions contradict each other, and particles moving past one another would behave like a liquid. Solid particles vibrate about fixed positions instead."}]},{"id":"069545f4-0c07-4122-bf36-3837472b4280","cardType":"basic","points":2,"front":"Why can a liquid flow and take its container's shape?","back":"Its particles can move past one another.","mcqOptions":[{"text":"Its particles can move past one another.","correct":true,"explanation":"Liquid particles remain close together but are not locked into fixed positions. They can move past one another, allowing the liquid to flow and take its container's shape."},{"text":"Its particles vibrate about fixed positions.","correct":false,"explanation":"Vibration about fixed positions describes a solid and explains why it keeps its shape. Liquid particles can move past one another."},{"text":"Its particles move quickly and spread out to fill the container.","correct":false,"explanation":"This describes gas behaviour. Liquid particles stay relatively close together, but they can move past one another and flow."},{"text":"Its particles are completely stationary throughout the liquid.","correct":false,"explanation":"Particles in every state have motion, so liquid particles are not stationary. Their ability to move past one another allows the liquid to flow."}]},{"id":"2bf8ea0c-1e33-46e5-91c0-d7a9f7792b99","cardType":"basic","points":2,"front":"Why does a gas have no fixed volume?","back":"Its particles move quickly and spread out to fill the container.","mcqOptions":[{"text":"Its particles move quickly and spread out to fill the container.","correct":true,"explanation":"Gas particles move rapidly and are far apart, spreading throughout any available space. Consequently, a gas has no fixed volume and fills its container."},{"text":"Its particles vibrate about fixed positions and cannot move past each other.","correct":false,"explanation":"This describes particles in a solid, which has a fixed volume and shape. Gas particles move quickly and spread out to fill the container."},{"text":"Its particles move slowly but remain tightly packed in one place.","correct":false,"explanation":"Tightly packed particles would keep a fixed volume, as in a solid or liquid. Gas particles are widely spaced and move quickly throughout the container."},{"text":"Its particles remain fixed but expand when the container changes size.","correct":false,"explanation":"Particles in a gas are not fixed in position. They move rapidly and spread out, allowing the gas to occupy the container's available volume."}]},{"id":"1a686ccf-b162-427c-9d32-d6e26f5255b1","cardType":"basic","points":2,"front":"Why are gases much less dense than solids and liquids?","back":"Far fewer particles, and therefore less mass, occupy each unit volume.","mcqOptions":[{"text":"Far fewer particles, and therefore less mass, occupy each unit volume.","correct":true,"explanation":"Gas particles are much farther apart than particles in solids and liquids. Therefore, each unit volume contains less mass, producing a much lower density."},{"text":"Far more particles, and therefore more mass, occupy each unit volume.","correct":false,"explanation":"Gas particles are spread widely apart, so fewer particles occupy each unit volume. That means less mass per unit volume and lower density."},{"text":"Particles are closer together, but each particle has less volume.","correct":false,"explanation":"The main difference is the large spacing between gas particles, not a smaller volume for each particle. Fewer particles per unit volume means less mass and lower density."},{"text":"The particles have no mass, so each unit volume has zero mass.","correct":false,"explanation":"Gas particles still have mass, even though they are widely separated. Fewer particles per unit volume gives less mass, but not zero mass."}]},{"id":"4c592dd8-b9e4-4073-9740-94ad82f1c2be","cardType":"basic","points":2,"front":"Why does density usually fall when a substance melts or boils?","back":"Particles spread further apart, increasing volume while mass stays constant, so density falls.","mcqOptions":[{"text":"Particles spread further apart, increasing volume while mass stays constant, so density falls.","correct":true,"explanation":"Melting or boiling usually increases particle separation. The mass is conserved while the volume increases, so dividing mass by volume gives a lower density."},{"text":"Particles move closer together, decreasing volume while mass stays constant, so density rises.","correct":false,"explanation":"Melting and boiling usually make particles further apart, not closer together. Increased volume with constant mass makes density fall rather than rise."},{"text":"Particles spread further apart, increasing mass while volume stays constant, so density rises.","correct":false,"explanation":"Changing state does not normally increase the amount of matter, so mass stays constant. The increased volume causes density to fall."},{"text":"Particles disappear, decreasing both mass and volume, so density stays constant.","correct":false,"explanation":"Particles do not disappear during a change of state. Mass is conserved, while increased particle separation usually increases volume and lowers density."}]},{"id":"57e47829-c6f3-4fdd-b84f-f3cef3cb056b","cardType":"basic","points":2,"front":"How is the volume of a regular cuboid found?","back":"Measure length, width and height, then use $V = l \\times w \\times h$.","mcqOptions":[{"text":"Measure length, width and height, then use $V = l \\times w \\times h$.","correct":true,"explanation":"A regular cuboid's volume is found by multiplying its three perpendicular dimensions: length, width and height. The result is expressed in cubic units."},{"text":"Measure length, width and height, then use $V = l + w + h$.","correct":false,"explanation":"Adding the dimensions gives a length-like quantity, not three-dimensional volume. Cuboid volume is calculated by multiplying length, width and height."},{"text":"Measure length, width and height, then use $V = 2(l + w + h)$.","correct":false,"explanation":"This expression calculates the cuboid's total edge length, not its volume. Volume requires the product $V = l \\times w \\times h$."},{"text":"Measure length, width and height, then use $V = \\dfrac{l \\times w}{h}$.","correct":false,"explanation":"Dividing by height gives the wrong relationship and incorrect units for volume. The three dimensions must be multiplied to find $V = l \\times w \\times h$."}]},{"id":"40ee8301-6870-4b5b-9366-1779c1a37d45","cardType":"basic","points":2,"front":"How is the volume of an irregular solid measured?","back":"Use water displacement; displaced water volume equals object volume.","mcqOptions":[{"text":"Use water displacement; displaced water volume equals object volume.","correct":true,"explanation":"An irregular solid cannot be measured accurately with a simple length formula. Submerging it displaces a volume of water equal to the object's volume."},{"text":"Use water displacement; displaced water volume equals object surface area.","correct":false,"explanation":"Water displacement measures the space occupied by the object, which is its volume, not its surface area. The displaced water volume equals object volume."},{"text":"Use a ruler; add the object's longest dimensions to find volume.","correct":false,"explanation":"Adding ruler measurements does not determine the volume of an irregular shape. Water displacement directly measures the object's volume from the water level change."},{"text":"Use its mass; divide the mass by its density without measuring water.","correct":false,"explanation":"Mass divided by known density can give volume, but the object's density would need to be known first. Water displacement measures an irregular object's volume directly."}]},{"id":"56f6c437-64dd-464a-85bd-368bacfa29e2","cardType":"basic","points":2,"front":"Why must a displacement can stop dripping before the object is lowered in?","back":"Earlier drips would be collected, making the measured volume too large.","mcqOptions":[{"text":"Earlier drips would be collected, making the measured volume too large.","correct":true,"explanation":"Allowing the displacement can to drip before lowering the object adds water that was not displaced by the object, so the collected volume would be greater than the object’s actual volume."},{"text":"Earlier drips would be collected, making the measured volume too small.","correct":false,"explanation":"The initial drips add water to the collection before the object enters, so they make the measured volume too large. The object’s displacement itself is not reduced."},{"text":"Earlier drips would be collected, making the measured mass too large.","correct":false,"explanation":"This experiment measures displaced volume, not the object’s mass. Drips collected before displacement increase the measured volume, which could then make the calculated density too small."},{"text":"Earlier drips would be collected, making the measured volume unchanged.","correct":false,"explanation":"Collected water from earlier drips is included in the final reading, so it changes the measured volume. The correct effect is that the measured volume becomes too large."}]},{"id":"c2617ffd-2e49-412b-a542-ced9ccab288c","cardType":"basic","points":2,"front":"Why must an irregular object be fully submerged during displacement?","back":"It must be fully submerged so all its volume displaces water.","mcqOptions":[{"text":"It must be fully submerged so all its volume displaces water.","correct":true,"explanation":"Only the part of the object below the water surface displaces water. Fully submerging it ensures the collected water represents the object’s entire volume."},{"text":"It must be fully submerged so none of its mass displaces water.","correct":false,"explanation":"Mass does not displace water; volume does. The important requirement is complete submersion so the object’s whole volume, rather than only part of it, displaces water."},{"text":"It must be partly submerged so all its volume displaces water.","correct":false,"explanation":"A partly submerged object displaces only the volume below the water surface. Full submersion is needed for the displaced volume to equal the object’s total volume."},{"text":"It must be fully submerged so all its density displaces water.","correct":false,"explanation":"Density is a property calculated from mass and volume and does not displace water. Submersion allows the object’s complete physical volume to be measured."}]},{"id":"525c8561-0126-45a5-b6b2-f1046525f3ba","cardType":"basic","points":2,"front":"How is the mass of a liquid found using a measuring cylinder?","back":"Mass of cylinder and liquid - mass of empty cylinder.","mcqOptions":[{"text":"Mass of cylinder and liquid - mass of empty cylinder.","correct":true,"explanation":"The combined mass includes both the measuring cylinder and the liquid. Subtracting the empty cylinder’s mass leaves the mass of the liquid alone."},{"text":"Mass of cylinder and liquid + mass of empty cylinder.","correct":false,"explanation":"Adding the empty cylinder’s mass counts the cylinder twice. Subtracting it from the combined measurement isolates the liquid’s mass."},{"text":"Mass of empty cylinder - mass of cylinder and liquid.","correct":false,"explanation":"This reverses the subtraction and would produce a negative value because the combined mass is greater. The combined mass minus the empty cylinder’s mass gives the liquid’s mass."},{"text":"Mass of cylinder and liquid ÷ mass of empty cylinder.","correct":false,"explanation":"Division gives a ratio rather than the liquid’s mass. The cylinder’s contribution must be removed from the combined measurement by subtraction."}]},{"id":"d9f9c28f-f068-45f4-a8cd-9bf08902a20e","cardType":"basic","points":2,"front":"How should liquid volume be read accurately in a measuring cylinder?","back":"Read the bottom of the meniscus at eye level.","mcqOptions":[{"text":"Read the bottom of the meniscus at eye level.","correct":true,"explanation":"Reading at eye level avoids parallax error, and the bottom of the curved liquid surface gives the correct volume for a concave meniscus."},{"text":"Read the top of the meniscus at eye level.","correct":false,"explanation":"Eye-level viewing prevents parallax, but the top of a concave meniscus is not the standard reading point. The bottom of the meniscus should be read."},{"text":"Read the bottom of the meniscus from above.","correct":false,"explanation":"The bottom is the correct point, but viewing from above creates parallax and usually makes the volume reading inaccurate. The eye must be level with the meniscus."},{"text":"Read the centre of the meniscus at eye level.","correct":false,"explanation":"Eye-level viewing is correct, but the centre is not the agreed reference point for a concave meniscus. The bottom of the meniscus should be used."}]},{"id":"adcde078-6dc4-4f9d-a146-80a0d69787aa","cardType":"basic","points":2,"front":"A block has mass $12\\ \\text{kg}$ and volume $0.004\\ \\text{m}^3$. Calculate its density.","back":"$3000\\ \\text{kg/m}^3$","mcqOptions":[{"text":"$3000\\ \\text{kg/m}^3$","correct":true,"explanation":"Density is mass divided by volume: $\\rho = \\frac{12\\ \\text{kg}}{0.004\\ \\text{m}^3} = 3000\\ \\text{kg/m}^3$."},{"text":"$48\\ \\text{kg/m}^3$","correct":false,"explanation":"Multiplying mass by volume instead of dividing gives this value, but density is calculated using $\\rho = \\frac{m}{V}$. The correct density is $3000\\ \\text{kg/m}^3$."},{"text":"$300\\ \\text{kg/m}^3$","correct":false,"explanation":"This results from mishandling the decimal in the volume by a factor of ten. Dividing $12\\ \\text{kg}$ by $0.004\\ \\text{m}^3$ gives $3000\\ \\text{kg/m}^3$."},{"text":"$0.00033\\ \\text{kg/m}^3$","correct":false,"explanation":"This reverses the density calculation by dividing volume by mass. Density requires mass divided by volume, giving $3000\\ \\text{kg/m}^3$."}]}]}],"examCountdown":{"examDate":"2027-05-25","paperLabel":"Paper 1"},"heading":"3.1.1 Density of materials","title":"3.1.1 Density of materials Flashcards","topbar":{"backHref":"/gcse/physics/aqa/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"015ba9ae-81c9-5976-bdf9-e528807cd7ad","walled":"$L39"}],"$L3a","$L3b"]