Q. A glass flask having mass 390 g and an interior volume of $500\ {cm}^{3}$ floats on water when it is less than half filled with water. The density of the material of the flask is
A) $0.8\ g{\ cc}^{- 1}$
B) $2.8\ g{\ cc}^{- 1}$
C) $1.8\ g\ {\ cc}^{- 1}$
D) $0.28\ g{\ cc}^{- 1}$
Explanation
(b) As the flask floats in water in less than half filled with water, it will float just fully submerged when half filled. In the situation,
mass of flask +mass of water in it$= V\sigma$
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$ie,\ 390 + 250 = V \times 1\ \ \ \ \ \ \ \ \ \ \left( as\ \sigma = 1\ g\ {cc}^{- 1} \right)$
ie, outer of volume of flask
$V = 640\ cc$
Now, as inner volume of flask is given to be 500 cc, so the volume of the material of flask $= 640 - 500 = 140\ cc.$ But as mass of flask is 390 g, so density of material of flask
$\rho = \frac{m}{v} = \frac{390}{140} = 2.8\ g\ {cc}^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.