Q81 / 100 · BITSAT 2024 (Memory Based Paper 1) · Physics

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

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

Solution

Let $V_1$ be, the volume immersed in water. $V_2$ be the volume immersed in oil. In equilibrium condition, $v_1 \rho_w g+v_2 \rho_0 g=\left(v_1+v_2\right) \rho_e g$ $v_1+\frac{v_2 \rho_0}{\rho_w}=\left(v_1+v_2\right) \frac{\rho_c}{\rho_w}$ $\Rightarrow v_1+0.8 v_2=0.9 v_1+0.9 v_2 \Rightarrow 0.1 v_1=0.1 v_2$ $\Rightarrow v_1: v_2=1: 1$

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

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