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

(a) u = 4v

(b) u = 2v

(c) v = u

(d) v = 4u

Answer 1

Correct option is (a) u = 4v

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