If a match box of size 5 cm \( \times \) 4 cm \( \times \) 1 cm is filled with nuclear matter, what will be its expected mass? The density of the nuclear matter is approximately \( 2.3 \times 10^{17}\,\mathrm{kg\,m^{-3}} \).
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 4.6 \times 10^{12}\,\mathrm{kg} \)
Nuclear matter has the same, enormous density in every nucleus, so the mass is the density times the volume. The density is in \( \mathrm{kg\,m^{-3}} \), so the volume must be in \( \mathrm{m^{3}} \).
\( \displaystyle V = 5 \times 4 \times 1\,\mathrm{cm^{3}} = 20\,\mathrm{cm^{3}} \)
\( \displaystyle V = 20\times10^{-6}\,\mathrm{m^{3}} = 2\times10^{-5}\,\mathrm{m^{3}} \)
\( \displaystyle m = \rho\,V = 2.3\times10^{17} \times 2\times10^{-5} = 4.6\times10^{12}\,\mathrm{kg} \)