Q68 / 90 · JEE Main 2024 (08 Apr Shift 2) · Physics

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil $=0.8$, specific gravity of ice $=0.9$) Figure

  • Correct answer
    A
    $1: 1$
  • B
    $5: 4$
  • C
    $8: 9$
  • D
    $9: 10$

Solution

$\begin{aligned} & \mathrm{v}_1=\text { volume immersed in water. } \\ & \mathrm{v}_2=\text { volume immersed in oil. } \\ & \mathrm{v}_1 \rho_{\mathrm{w}} \mathrm{g}+\mathrm{v}_2 \rho_{\mathrm{o}} \mathrm{g}=\left(\mathrm{v}_1+\mathrm{v}_2\right) \rho_{\mathrm{c}} \mathrm{g} \\ & \mathrm{v}_1+\frac{\mathrm{v}_2 \rho_{\mathrm{o}}}{\rho_{\mathrm{w}}}=\left(\mathrm{v}_1+\mathrm{v}_2\right) \frac{\rho_{\mathrm{c}}}{\rho_{\mathrm{w}}} \\ & =\mathrm{v}_1+0.8 \mathrm{v}_2=0.9 \mathrm{v}_1+0.9 \mathrm{v}_2 \\ & =0.1 \mathrm{v}_1=0.1 \mathrm{v}_2 \\ & \mathrm{v}_1: \mathrm{v}_2=1: 1\end{aligned}$

Hence, the correct answer is option: 'A'.

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