question_answer

A glass flask having mass 390 g and an interior volume of \[\text{500 c}{{\text{m}}^{\text{3}}}\]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         

B)  2.8 g/cc

C)  1.8 g/cc         

D)  0.28 g/cc

Correct Answer: B

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.,  \[390+250=V\times 1\] (as )   390 + 250 = V x 1    (as \[\sigma =1g/cc\]) i.e., outer 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 \[\rho =\frac{m}{V}\] \[=\frac{390}{140}=2.8\,g/cc\]