Let x, y be the volumes; m, n be the masses of two metallic cubes P and Q

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?

  1. u = 4v
  2. u = 2v
  3. v = u
  4. v = 4u

Answer: A

Explanation

Given: Volume of P = x; Volume of Q = y; Mass of P = m; Mass of Q = n

It is given that, Mass of Q = 2 × Mass of P

Or n = 2m

Also, each side of Q is two times that of P.

Let each side of P be a units and that of Q be 2a units.

So, x = a3

And y = (2a)3 = 8a3

According to the question,

u = m/x

or u = m/a3 (1)

And v = n/y

or v = 2m/8a3 = m/4a3 (2)

From (1) and (2), we get:

u/v = 4

or u = 4v

  • Exam Year: 2020