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(B) The apparent weight $w$ of a body immersed in a liquid is given by $w = V_s(\rho_s - \rho_w)g$,where $V_s$ is the volume of the sphere,$\rho_s$ is

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$w_1 < w_2$

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(B) The apparent weight $w$ of a body immersed in a liquid is given by $w = V_s(\rho_s - \rho_w)g$,where $V_s$ is the volume of the sphere,$\rho_s$ is the density of the sphere,and $\rho_w$ is the density of water.Since the volume $V_s$ increases with temperature,we consider the mass $M = V_s \rho_s$ to be constant. Thus,$w = Mg - V_s \rho_w g$.As temperature increases from $0^{\circ} C$ to $50^{\circ} C$,the volume of the sphere $V_s$ increases,and the density of water $\rho_w$ decreases significantly because the coefficient of cubical expansion of water is greater than that of the metal.Since $\rho_w$ decreases more rapidly than the volume $V_s$ increases,the buoyant force $F_B = V_s \rho_w g$ decreases as temperature increases.Therefore,the apparent weight $w = Mg - F_B$ increases with temperature.Thus,$w_2 > w_1$ or $w_1 < w_2$.

$A$ metal sphere immersed in water weighs $w_1$ at $0^{\circ} C$ and $w_2$ at $50^{\circ} C$. The coefficient of cubical expansion of the metal is less than that of water. Then

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