Question

For the uranium nucleus. Find the relation between the mass and the volume
A. \[m \propto v\]
B. \[m \propto \sqrt v \]
C. \[m \propto {v^2}\]
D. \[m \propto \dfrac{1}{v}\]

Answer 1

Hint: The above problem can be resolved using the mathematical formula for the density of any substance. The relation provides significant knowledge of the mass as well as the volume occupied by the substance. When a substance possesses some definite value of its density, one can easily predict the relation between the mass and volume for the given substance.


Complete step by step answer
Consider an uranium nucleus of mass m and volume v. Then applying the mathematical formula for the density of the uranium nucleus as,
\[\rho = \dfrac{m}{v}...................\left( 1 \right)\]
Here, \[\rho \] denotes the density of the uranium nucleus, which cannot be changed and remains constant.
Then, the equation 1 for the constant value of density is given as,
\[\begin{array}{l}
\rho = \dfrac{m}{v}\\
m \propto v........................\left( 2 \right)
\end{array}\]
It is clear from equation 2 that the mass of the uranium nucleus and its volume has the linear relationship.
Therefore, the mass and the volume of the uranium nucleus is related as, \[m \propto v\]and option A is correct.


Note: To resolve the given problem, one must understand that any substance's density depends on the mass of the substance and the volume of matter occupied within the substance. In this case, the uranium nucleus of specific mass and volume are observed to have a constant density value. The significant relation for the mass and volume can be determined. Moreover, for many cases, the masses have their fixed value, and other parameters vary accordingly.