UPSC CDS I 2019 GK Paper

Concept:Buoyant force depends on volume. Equal apparent weight in water implies the object with larger volume (lower density) has a larger actual weight in air.Explanation:Given: Two pieces, gold and silver, have equal weight when fully submerged in water.Density of gold ($\rho_g$) > density of silver ($\rho_s$).Let $W_g$ and $W_s$ be weights in air, $V_g$ and $V_s$ be volumes.Apparent weight in water = weight in air – buoyant force.Buoyant force = weight of displaced water = $V \cdot \rho_w g$.Equality in water: $W_g - V_g \rho_w g = W_s - V_s \rho_w g$.Since $W = \rho V g$, we get $\rho_g V_g - \rho_w V_g = \rho_s V_s - \rho_w V_s$.Thus $V_g (\rho_g - \rho_w) = V_s (\rho_s - \rho_w)$.Because $\rho_g > \rho_s$, we have $(\rho_g - \rho_w) > (\rho_s - \rho_w)$, so $V_g < V_s$.Silver has larger volume, hence larger buoyant force.To have the same apparent weight, the silver piece must be heavier in air to compensate for the larger upward push.Mathematically, from the equality: $\rho_g V_g - \rho_s V_s = \rho_w (V_g - V_s)$.The right side is negative (since $V_g < V_s$), so $\rho_g V_g < \rho_s V_s$, i.e., $W_g < W_s$.Therefore, silver weighs more in air.Answer:The silver piece will weigh more. Option B is correct.