JEE Main 20248 AprilEvening Shift

Exam: JEE Main
Year: 2024
Date: 8 April
Shift: Evening Shift
Subject: Physics
Chapter: Mechanical Properties of Fluids

JEE Main 2024 · 8 April · Evening Shift · Physics · Mechanical Properties of Fluids

A cube of ice floats partly in water and partly in kerosene oil....

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

)

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that

Options

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

Correct answer

A. $1: 1$

Step-by-step solution

\begin{aligned} & \mathrm{v}_1=\text{ volume immersed\text{ 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}

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