A solid cube is floating in a liquid. The coe | vedclass

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(B) For a floating object,the weight of the displaced liquid equals the weight of the object: $V_{sub} \rho_{liq} g = V_{cube} \rho_{cube} g$,where $V

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$\gamma > 3\alpha$

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(B) For a floating object,the weight of the displaced liquid equals the weight of the object: $V_{sub} \rho_{liq} g = V_{cube} \rho_{cube} g$,where $V_{sub}$ is the submerged volume of the cube.This implies $V_{sub} \rho_{liq} = V_{cube} \rho_{cube}$.Let the temperature increase by $\Delta T$. The new volumes and densities are:$V'_{cube} = V_{cube}(1 + 3\alpha \Delta T)$$V'_{liq} = V_{liq}(1 + \gamma \Delta T) \implies \rho'_{liq} = \frac{\rho_{liq}}{1 + \gamma \Delta T} \approx \rho_{liq}(1 - \gamma \Delta T)$For the cube to sink,the fraction of the submerged volume must increase,meaning the density of the liquid must decrease more rapidly than the density of the cube,or effectively,the liquid must expand more than the cube.The condition for sinking is that the liquid expands more than the cube,i.e.,the volume expansion coefficient of the liquid must be greater than the volume expansion coefficient of the solid cube.The volume expansion coefficient of the cube is $3\alpha$.Therefore,the cube will sink if $\gamma > 3\alpha$.

$A$ solid cube is floating in a liquid. The coefficient of linear expansion of the cube is $\alpha$ and the coefficient of volume expansion of the liquid is $\gamma$. On increasing the temperature of the (liquid + cube) system,the cube will sink if

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