Question

A cubical block of wood of specific gravity $0.5$ and chunk of concrete Of specific gravity $2.5$ are fastened together. The ratio of mass of concrete to the mass of wood which makes the combination to float with its entire volume submerged in water is

• A. $\frac{5}{3}$
• B. $\frac{6}{5}$
• C. $\frac{5}{2}$
• D. $\frac{4}{3}$

Answer 1

The correct option is A $\frac{5}{3}$

$\text{Let vol. of wood}=x$

$\text{vol. of concrete}=y$

$\text{vol. of water displace}=x+y\text{.}$

$\text{mass of (wood concrete)}=\text{mass of water}$

$0.5x+2\cdot 5y=(x+y)1$

$1.5xy=0.5x$

$3y=x.$

$\frac{\text{Mass wood}}{\text{mass concrete}}=\frac{0.5\times x}{2.5\times y}$

$=\frac{1.5y}{2.5y}=\frac{3}{5}$

$=\frac{\text{Mass concrete}}{\text{mass wood}}=\frac{5}{3}$

Ans: (A)