Measurement of Matter — Practice Exercises: 19 MCQs with answers

A numerical value together with a unit

A measurement is meaningful only when both the number and the unit are stated. A number without a unit does not tell you what was measured.

kilogram

The SI base unit of mass is the kilogram (kg). The gram is a submultiple, and the newton is the unit of force (weight).

Length

Length is the base quantity measured in metres. Mass is measured in kilograms, time in seconds, and temperature in kelvin.

2500 g

Since $1\ \text{kg} = 1000\ \text{g}$, multiply by 1000: $2.5 \times 1000 = 2500\ \text{g}$.

kelvin

The SI base unit of temperature is the kelvin (K). Degree Celsius and degree Fahrenheit are other temperature scales, and the joule is a unit of energy.

True

The SI unit of density is $\text{kg/m}^3$, though $\text{g/cm}^3$ is commonly used in laboratory work.

$2.7\ \text{g/cm}^3$

Density $\rho = m/V = 270/100 = 2.7\ \text{g/cm}^3$. This is the density of aluminium, a useful sanity check.

$1000\ \text{kg/m}^3$

$1\ \text{g/cm}^3 = \frac{10^{-3}\ \text{kg}}{10^{-6}\ \text{m}^3} = 10^3\ \text{kg/m}^3 = 1000\ \text{kg/m}^3$.

Too many decimal places are reported for the instrument's precision

The least count of 0.1 cm means the ruler cannot reliably measure beyond one decimal place. Reporting 4.567 cm invents precision that the instrument does not have.

3

Leading zeros are not significant. The digits 4, 2, and the trailing zero after the decimal are significant, giving 3 significant figures.

5 kg

Weight $W = mg$, so $m = W/g = 49/9.8 = 5\ \text{kg}$. Mass is in kilograms; the weight is in newtons.

A screw gauge with least count 0.001 cm

The screw gauge has the smallest least count (0.001 cm), so it can measure the smallest difference and is the most precise of the four.

15 mL

The volume of the stone equals the volume of water displaced: $65 - 50 = 15\ \text{mL}$ (or $15\ \text{cm}^3$).

298.15 K

$T(\text{K}) = T(^\circ\text{C}) + 273.15 = 25 + 273.15 = 298.15\ \text{K}$.

Convert the volume to $\text{m}^3$ so units are consistent

Formulas require consistent units. Convert $\text{cm}^3$ to $\text{m}^3$ (using $1\ \text{cm}^3 = 10^{-6}\ \text{m}^3$) before multiplying by density to get mass in kilograms.

The value matches aluminium's known density, so the claim is reasonable but not conclusive

A density of $2.7\ \text{g/cm}^3$ is consistent with aluminium, so the claim is plausible. However, density alone does not uniquely identify a substance; other properties may be needed for certainty.

1000 kg/m³

To find the density, first convert the mass to kg: 500 g = 0.5 kg. The volume in liters must be converted to cubic meters: 0.5 L = 0.5 × 10^{-3} m³. Therefore, density is calculated as $$\rho = \frac{0.5\ \text{kg}}{0.5 \times 10^{-3}\ \text{m}^3} = 1000\ \text{kg/m}^3$$.

1.2 g/cm³

Density is calculated using the formula $$\rho = \frac{m}{V}$$. Here, mass is 600 g and volume is 300 cm³, so $$\rho = \frac{600\ \text{g}}{300\ \text{cm}^3} = 2.0\ \text{g/cm}^3$$.

1570 g

First, calculate the volume of the cylinder using the formula $$V = \pi r^2 h$$. Here, $$V = \pi (5\ \text{cm})^2 (20\ \text{cm}) = 500\ \text{cm}^3$$. Then, calculate the mass: $$m = \rho V = 1.5\ \text{g/cm}^3 \times 500\ \text{cm}^3 = 750\ \text{g}$$.