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  • A piece of ice, with a stone frozen inside it, is floating in water contained in a beaker. When the ice melts, the level of water in the beakerOption: 1

A piece of ice, with a stone frozen inside it, is floating in water contained in a beaker. When the ice melts, the level of water in the beaker

Option: 1

rises
 


Option: 2

falls
 


Option: 3

remains unchanged
 


Option: 4

falls at first and then rises to the same height as before.


Answers (1)

best_answer

Let the mass of ice be \mathrm{m_1 } and the mass of stone be \mathrm{m_2}. The mass of the displaced water is equal to \mathrm{\left(m_1+m_2\right).} If \mathrm{\rho} is the density of water, the volume of water displaced is

                                         \mathrm{ V=\left(m_1+m_2\right) / \rho }
When the ice melts, additional volume of water obtained is \mathrm{m_1 / \rho}. The stone sinks in water, and displaces a volume of water equal to its own volume, which is \mathrm{ m_2 / \rho_s}  where \mathrm{ \rho_s} is the density of stone. Thus the total volume of extra water is

\mathrm{ V^{\prime}=\frac{m_1}{\rho}+\frac{m_2}{\rho_s}}

Since \mathrm{\quad \rho_s>\rho, \frac{1}{\rho_s}<\frac{1}{\rho}}

 

\mathrm{\therefore V^{\prime}<V}. Therefore, level of water in beaker decreases.

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