Question

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 the mass of Q is two times that of P. Let u = m/x and v = n/y. Which one of the following is correct? 
1. u = 4v
2. u = 2v
3. v = u 
4. v = 4u 

Answer 1

Correct Answer - Option 1 : u = 4v

Given :

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 the mass of Q is two times that of P

Formula used :

The volume of a cube = side³ 

Calculations :

Let the side of cube P be 'a' 

Let the side of cube Q be '2a' 

Volume of cube P(x) = a³

Volume of cube Q(y) = (2a)³ = 8a³

Mass of P(m) = c 

Mass of Q(n) = 2c (mass of Q is 2 times the mass of P)

Now,

u = m/x = c/a³ and

v = n/y = (2c)/8a³ = (c)/4a³

Here, v = u/4 

∴ Option 1 is the correct answer.