A glass flask having mass 390 g and an interior volume of $500 \mathrm{~cm}^3$ floats on water when it is less than half filled with water. The density of material of the flask is

• A

  $0.8 \mathrm{~g} / \mathrm{cc}$
• Correct answer
  B

  $2.8 \mathrm{~g} / \mathrm{cc}$
• C

  $1.8 \mathrm{~g} / \mathrm{cc}$
• D

  $0.28 \mathrm{~g} / \mathrm{cc}$

Solution

As the flask floats in water when less than half filled with water, it will float just fully submerged when half filled. In this situation, mass of flask + mass of water in it $=V \sigma$ $i e$,$390+250=V \times 1(\text { as } \sigma=1 \mathrm{~g} / \mathrm{cc})$
$i e$, outer volume of flask $V=640 \mathrm{cc}$ Now as inner volume of flask is given to be 500 cc , so the volume of the material of flask $=640-500=140 \mathrm{cc}$. But as mass of flask is 390 g , so density of material of flask $\rho=\frac{m}{V}=\frac{390}{140}=2.8 \mathrm{~g} / \mathrm{cc}$

Hence, the correct answer is option: 'B'.