Let $x, y$ be the volumes; $m, n$ be the masses of two metallic cubes P and Q respectively. Each side of 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?
$u = 4v$
$u = 2v$
$v = u$
$v = 4u$
Solution
Let side of P be $a$, so $x = a^3$. Side of Q is $2a$, so $y = (2a)^3 = 8a^3 = 8x$. Mass of Q $= 2m$, so $n = 2m$. Then $u = m/x$ and $v = n/y = 2m/(8x) = m/(4x) = u/4$. Therefore $u = 4v$.