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  • A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density 0.8 and with its vertex submerged. When another liquid of relative density <img alt="\mathrm

A hollow cone floats with its axis vertical upto one-third of its height in a liquid of relative density 0.8 and with its vertex submerged. When another liquid of relative density \mathrm{\rho } is filled in it upto one-third of its height, the cone floats upto half its vertical height. The height of the cone is \mathrm{0.10 \mathrm{~m}} and radius of the circular base is 0.05 \mathrm{~m}. The specific gravity \mathrm{\rho } is given by

Option: 1

1.0


Option: 2

1.5


Option: 3

2.1


Option: 4

1.9


Answers (1)

best_answer

\mathrm{\begin{aligned} & \frac{1}{3} \pi r^2 h \rho_c g=\frac{1}{3} \pi(r / 3)^2 \frac{h}{3}(0.8) g \\ & \rho_c=\frac{0.8}{27} \end{aligned}}

\mathrm{\frac{1}{3} \pi r^2 h \rho_c g=\frac{1}{3} \pi\left(\frac{r}{6}\right)^2 \frac{h}{6} \times 0.8 \times g+}

\mathrm{\frac{1}{3} \pi\left[\left(\frac{r}{2}\right)^2 \frac{h}{2}-\left(\frac{r}{6}\right)^2 \frac{h}{6}\right] \rho g}

\mathrm{\Rightarrow \frac{0.8}{27}=\frac{0.8}{36 \times 6}+\left[\frac{1}{8}-\frac{1}{36 \times 6}\right] \rho \quad \rho=1.9}

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