JEE Main & Advanced
Physics
Fluid Mechanics, Surface Tension & Viscosity / द्रव यांत्रिकी, भूतल तनाव और चिपचिपापन
Question Bank
Critical Thinking
question_answer
A vessel contains oil (density = 0.8 gm/cm3) over mercury (density = 13.6 gm/cm3). A homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in gm/cm3 is [IIT-JEE 1988]
A) 3.3
B) 6.4
C) 7.2
D) 12.8
Correct Answer:
C
Solution :
As the sphere floats in the liquid. Therefore its weight will be equal to the upthrust force on it Weight of sphere \[=\frac{4}{3}\pi {{R}^{3}}\rho g\] ?(i) Upthrust due to oil and mercury \[=\frac{2}{3}\pi {{R}^{3}}\times {{\sigma }_{oil}}g+\frac{2}{3}\pi {{R}^{3}}{{\sigma }_{Hg}}g\] ?(ii) Equating (i) and (ii) \[\frac{4}{3}\pi {{R}^{3}}\rho g=\frac{2}{3}\pi {{R}^{3}}0.8g+\frac{2}{3}\pi {{R}^{3}}\times 13.6g\]\[\Rightarrow 2\rho =0.8+13.6=14.4\Rightarrow \rho =7.2\]