Question

A metal block is suspended in an empty tank from a scale indicating a weight of $W$. The tank is then filled with water until the block is covered. If the density of the metal is three times the density of water, what apparent weight of the block does the scale now read?

• A. $1/2W$
• B. $2/3W$
• C. $W$
• D. $3/2w$

Answer 1

The correct option is B $2/3W$

Let density water $=\rho$

$\therefore$ Density of block $=3\rho$

Let mass of block $=m$

$\therefore W=mg$

volume of block $\left(v\right)=\frac{m}{3\rho }$

Apparent weight $\left(w^{\prime }\right)=mg-\rho vg$

$w^{\prime }=mg-\rho \left(\frac{m}{3\rho }\right)g$

$w^{\prime }=\frac{2mg}{3}-\left(ii\right)$

from eq: (i) and (ii)

$w^{\prime }=\frac{2}{3}w$