Properties Of Solids And Liquids Question 277
Question: Two solids A and Bfloat in water. It is observed that A floats with $ \frac{1}{2} $ of its body immersed in water and B floats with $ \frac{1}{4} $ of its volume above the water level. The ratio of the density of A to that of B is
Options:
A)4 : 3
B)2 : 3
C)3 : 4
D)1 : 2
Show Answer
Answer:
Correct Answer: B
Solution:
Upthrust = weight of body For A, $ \frac{V _{A}}{2}\times {\rho _{W}}\times g=V _{A}\times {\rho _{A}}\times g\Rightarrow {\rho _{A}}=\frac{{\rho _{W}}}{2} $
For B, $ \frac{3}{4}V _{B}\times {\rho _{W}}\times g=V _{B}\times {\rho _{B}}\times g\Rightarrow {\rho _{B}}=\frac{3}{4}{\rho _{W}} $
(Since 1/4 of volume of B is above the water surface) \ $ \frac{{\rho _{A}}}{{\rho _{B}}}=\frac{{\rho _{W}}/2}{3/4\ {\rho _{W}}}=\frac{2}{3} $
