Question

For a uranium nucleus how does its mass vary with volume?
$
  {\text{A}}{\text{. m}} \propto V \\
  {\text{B}}{\text{. m}} \propto \dfrac{1}{V} \\
  {\text{C}}{\text{. m}} \propto {\sqrt V} \\
  {\text{D}}{\text{. m}} \propto {V^2} \\
 $

Answer 1

Hint: To solve this question we have to first make sure we are talking about uniform nucleus so that density is constant then we can easily answer that how does uranium nucleus mass vary with volume.
Formula used: ${\text{density = }}\dfrac{{{\text{mass}}}}{{{\text{volume}}}}$

Complete Step-by-Step solution:
So in this question if we have knowledge that our nucleus is uniform that means density will be constant and then using formula ${\text{density = }}\dfrac{{{\text{mass}}}}{{{\text{volume}}}}$ we can easily answer uranium nucleus dependency on volume.
${\text{density = }}\dfrac{{{\text{mass}}}}{{{\text{volume}}}}$
We can write it as:
${\text{mass = density }} \times {\text{ volume}}$
As we know density is constant for uniform nucleus so we can write
${\text{mass }} \propto {\text{ Volume}}$
Hence option A is the correct option.

Note: Whenever we get this type of question the key concept of solving is we have to understand all the conditions in which we can say is it proportional or not that means we have to first assume the condition in which we are talking about proportionality.