Question

Mass of a body is \[210\] gm and its density is \[7.981\] $gm/{cm^3}$. What will be its volume with regard to significant digits?
A. $26.312\,c{{m}^{3}}$
B. $26\,c{{m}^{3}}$
C. $27\,c{{m}^{3}}$
D. $26.3\,c{{m}^{3}}$

Answer 1

Hint: We know that we use dimension to convert the unit of volume from one system (here CGS) to another (SI). The relative volume of any metal is given by the ratio of the volume of the metal in the air to the volume of water and the relative volume of the unknown liquid is given by the ratio of the volume of that fluid to the volume of water.

Complete step by step answer:
As we know that the relationship between physical quantities with the help of dimensions and units of measurement is termed as dimensional analysis. Dimensional analysis is essential because it keeps the units the same, helping us perform mathematical calculations smoothly.

The main idea in Dimensional Analysis is to create a conversion ratio unit factor which has the units you want in the numerator and the units you already have in the denominator. The relationship between physical quantities with the help of their dimensions and units of measurement is called dimensional analysis. Here the density is the ratio of mass and volume.
$d=\dfrac{m}{V} \\
\Rightarrow V=\dfrac{m}{d}$
On further substitution we get;
$V=\dfrac{210}{7.981} \\
\therefore V =26.312\,c{{m}^{3}}$
Thus, the least number of significant figures in any number of the problem determines the number of significant figures in the answer and the answer is $26.3.$

Therefore, the correct answer is option D.

Note:Remember that the relative volume of any substance is given by the ratio of the density of that substance to the density of another standard substance. We use dimensional analysis to convert a unit from one form to another.