Let x, y be the volumes; m, n be the masses of two metallic cubes P and Q respectively. Each side of Q is two times that of P and mass of q is two times that of P. Let u = m/x and v = n/y. Which one of the following is correct?

Correct Option (1)

Let 'a' represent the side length of cube P. Consequently, the side length of cube Q is 2a.

• The volume of cube P, denoted as x, is a³.
• The volume of cube Q, denoted as y, is (2a)³ = 8a³.
• The mass of cube P is given as m.
• The mass of cube Q, denoted as n, is given as 2m.

Now, we define u and v:

• u = m/x = m/a³
• v = n/y = (2m)/(8a³) = m/(4a³)

Comparing u and v:

u/v = (m/a³) / (m/(4a³)) = (m/a³) * (4a³/m) = 4

Therefore, u = 4v.

Incorrect Options:

Options 2, 3, and 4 are incorrect because the derived relationship, based on the given parameters and definitions of u and v, unequivocally establishes that u = 4v. These options propose alternative relationships that are inconsistent with the mathematical derivation.