/edexcel/questions","basePath":"/gcse/physics/edexcel/density-and-states-of-matter/questions","formulaUrl":null,"initialIndex":69,"initialQuestionWindow":[{"id":"d6dc6427-1d93-44a9-ad8b-8fe1e6c19ae5","revisionId":"1b0d8e42-a89e-42b3-ba7c-8cbfe4afc26a","questionNumber":null,"questionType":"LA","specification":"A small metal sample has a mass of $6.45 \\times 10^{-2}\\text{ kg}$ and a volume of $7.50 \\times 10^{-6}\\text{ m}^3$.","difficulty":4,"difficultyBand":"easy","totalMarks":3,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"64d37cbe-2a7c-49ae-ba7f-3bd8c620e566","label":null,"content":"Calculate the density, $\\rho$, of the metal sample.\n\nUse the equation:\n\n$$\\rho = \\frac{m}{V}$$\n\nState the unit.","markscheme":"- Substitutes the values into the density equation: $\\rho = \\frac{6.45 \\times 10^{-2}}{7.50 \\times 10^{-6}}$ M1\n- Calculates the density as $8600$ (or $8.6 \\times 10^3$) A1\n- States the correct unit of density: $\\text{kg/m}^3$ (or $\\text{kg}\\text{ m}^{-3}$) B1","marks":3,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"density_calculation","label":"Use the density equation","steps":[{"type":"text","order":0,"title":"Identify the quantities","content":"The mass is already in kilograms and the volume is already in cubic metres, so no unit conversion is needed. Use the given density equation, where $m$ is mass and $V$ is volume.","highlights":[{"text":"mass of $6.45 \\times 10^{-2}\\text{ kg}$","location":"specification"},{"text":"volume of $7.50 \\times 10^{-6}\\text{ m}^3$","location":"specification"},{"text":"$$$\\rho = \\frac{m}{V}$$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\rho=\\frac{\\htmlData{anchor=mass}{6.45\\times10^{-2}}}{\\htmlData{anchor=volume}{7.50\\times10^{-6}}}"},{"latex":"\\rho=\\left(\\frac{6.45}{7.50}\\right)\\times10^{-2-(-6)}"},{"latex":"\\rho=0.86\\times10^{4}"},{"latex":"\\rho=\\htmlData{anchor=density}{8.6\\times10^{3}}"}],"highlights":[{"color":"green","style":"box","anchor":"density"}]},"order":1,"title":"Calculate the density","description":"Substituting the given mass and volume into the density equation earns M1. Dividing to get the final value earns A1."},{"type":"text","order":2,"title":"State the unit","content":"Density is mass divided by volume, so its unit is kilograms per cubic metre: $$\\text{kg/m}^3$$ This earns **B1**.\n\nTherefore, state the answer as $$\\rho=8.6\\times10^3\\ \\text{kg/m}^3$$"}]}],"generatedAt":"2026-07-22T09:30:40.100Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null},{"id":"d8664d71-3ab6-4e71-8e30-b06e66356de4","revisionId":"fac13c41-5cfb-4a0a-8e65-615f170f406a","questionNumber":null,"questionType":"LA","specification":"A high-purity copper busbar used in an electrical substation is machined in the shape of a rectangular cuboid with dimensions $15\\text{ mm}$ by $40\\text{ mm}$ by $80\\text{ mm}$.\n\nThe busbar has a mass of $427.2\\text{ g}$.","difficulty":4,"difficultyBand":"easy","totalMarks":2,"sourceTitle":null,"calculatorUse":null,"parts":[{"id":"62582bc3-ec9a-4cdd-82ce-4ea4f15a7997","label":null,"content":"Calculate the density of this copper sample in $\\text{g/cm}^3$.","markscheme":"- Converts the dimensions to $\\text{cm}$ ($1.5\\text{ cm}$, $4.0\\text{ cm}$, $8.0\\text{ cm}$) to find the volume: $V = 1.5 \\times 4.0 \\times 8.0 = 48\\text{ cm}^3$ (or calculates volume as $48,000\\text{ mm}^3$ and divides by $1000$) M1\n- Calculates the density as $\\text{density} = \\frac{427.2}{48} = 8.9\\text{ g/cm}^3$ A1","marks":2,"order":0,"markingRubric":null,"explanation":{"methods":[{"id":"calculate_density","label":"Calculate density","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"15\\text{ mm}=1.5\\text{ cm}"},{"latex":"40\\text{ mm}=4.0\\text{ cm}"},{"latex":"80\\text{ mm}=8.0\\text{ cm}"},{"latex":"V=1.5\\times4.0\\times8.0\\text{ cm}^3"},{"latex":"V=48\\text{ cm}^3"}]},"order":1,"titl

Density and states of matter

Question 43

Density and states of matter Questions

Density and states of matter

Question 43

Density and states of matter Questions