Question

A piece of wax weighs $x$ gm in air. A piece of metal weighs $y$ gm in water. It is tied to the wax and both together weigh $z$ gm in water. Then, the specific gravity of wax, $(z<y)$, is:

• A. $\frac{x}{y}$
• B. $\frac{y}{x}$
• C. $\frac{x}{x-(z-y)}$
• D. $\frac{x}{x-z}$

Answer 1

Answer: (C)

$\frac{x}{x-(z-y)}$
Given mass of wax in air = x
Also, mass of metal in water =
And, mass of wax and metal in water =

Hence, mass of wax in water = z-y
We can consider, mass of wax in water = mass of wax in air - upthrust due to water
Upthrust = specific gravity of water $\times$ volume of wax
Upthrust = x - (z - y)
But specific gravity of water is 1, so Upthrust is effectively volume of wax
Mass of wax = x
Hence, specific gravity of wax = $\frac{x}{x-(z-y)}$