A balloon of mass m contains water of mass M. | vedclass

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(D) The total mass of the balloon system is $M_{total} = M + m$.When the balloon is completely immersed in water, it displaces a volume of water equal

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$m$

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(D) The total mass of the balloon system is $M_{total} = M + m$.When the balloon is completely immersed in water, it displaces a volume of water equal to its own volume.Since the balloon contains water of mass $M$ and the balloon material itself has mass $m$, the total volume $V$ of the system is the volume of the water $M$ plus the volume of the balloon material $m$.However, the density of the water inside is the same as the density of the surrounding water.According to Archimedes' Principle, the buoyant force $F_B$ acting on the balloon is equal to the weight of the displaced water: $F_B = (M + \rho_{material} \cdot V_{material})g$, where $\rho_{material} \cdot V_{material} = m$.Thus, $F_B = (M + m)g$.The apparent weight $W_{app}$ is given by $W_{app} = W_{actual} - F_B = (M + m)g - (M + m)g = 0$.Wait, if the balloon material has negligible volume, the buoyant force is equal to the weight of the water displaced, which is $M \cdot g$. The total weight is $(M + m)g$. The apparent weight is $(M + m)g - Mg = mg$.Therefore, the apparent mass is $m$.

$A$ balloon of mass $m$ contains water of mass $M$. If it is completely immersed in water, find the apparent mass of the balloon with water in it.

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