- Home
- Standard 11
- Physics
9-1.Fluid Mechanics
hard
A vessel contains oil (density =$ 0.8 \;gm/cm^3$) over mercury (density = $13.6\; gm/cm^3$). 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/cm^3$ is
A
$3.3$
B
$6.4$
C
$ 7.2$
D
$12.8$
(IIT-1998)
Solution
(c)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) …… (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$
Standard 11
Physics
