Assertion: A piece of ice, with a stone frozen inside it, floats on water in a beaker. When the ice melts, the level of water in the beaker decreases.
Reason: Density of stone is more than water.
(A) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
(B) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
(C) Assertion is correct but Reason is incorrect.
(D) Both Assertion and Reason are incorrect.
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Hint:There will be heat transfer occurring from the water to ice as there is a temperature difference, hence, the ice will melt. Consider the densities of water and ice, compare them and accordingly determine the volume of the water that will be produced after the whole ice is melted. Following the procedure, you can determine whether the level of water will rise or fall.
Complete step by step solution:
The densities of water and ice are equal to $1$$gc{m^{ - 3}}$ and $0.917$$gc{m^{ - 3}}$
respectively.
Now, density is defined as the ratio of the mass and volume. It is the measure of mass per unit volume. Density is denoted by $\rho $ and is equal to \[\dfrac{m}{V}\]. So, in our case, the ice melts and is converted into water. You can notice that in the overall process of melting, the mass of water that will be produced due to melting of ice will be equal to the mass of the ice.
Mathematically, we have,
\[
{m_{ice}} = {m_{waterproduced}} \\
{\rho _{ice}}{V_{ice}} = {\rho _{waterproduced}}{V_{waterproduced}} \\
\dfrac{{{V_{waterproduced}}}}{{{V_{ice}}}} = \dfrac{{{\rho _{ice}}}}{{{\rho _{waterproduced}}}}
\\
\]
Substituting the value of densities of water and ice, we get
\[\dfrac{{{V_{waterproduced}}}}{{{V_{ice}}}} = \dfrac{{0.917}}{1} = 0.917\]. As you can see that
\[\dfrac{{{V_{waterproduced}}}}{{{V_{ice}}}} < 1 \to {V_{waterproduced}} < {V_{ice}}\].
So, the volume that will be produced from the ice will be less than the actual volume of the ice. Now, if you consider the stone, it will not make a significant effect on the level of the water as the ice was already floating on the water. It will just sink down. Therefore, we can say that the water level will decrease after the ice has melted.
Therefore, both Assertion and Reason are correct and Reason is the correct explanation for
Assertion.
Thus,the correct option is (A).
Note:Always remember the values of the densities of water and ice, it will help you to solve many questions related to the ice water system. Also keep in mind the method we used to determine the volume produced from the melted ice, the mass will remain the same even after the change of state.
Complete step by step solution:
The densities of water and ice are equal to $1$$gc{m^{ - 3}}$ and $0.917$$gc{m^{ - 3}}$
respectively.
Now, density is defined as the ratio of the mass and volume. It is the measure of mass per unit volume. Density is denoted by $\rho $ and is equal to \[\dfrac{m}{V}\]. So, in our case, the ice melts and is converted into water. You can notice that in the overall process of melting, the mass of water that will be produced due to melting of ice will be equal to the mass of the ice.
Mathematically, we have,
\[
{m_{ice}} = {m_{waterproduced}} \\
{\rho _{ice}}{V_{ice}} = {\rho _{waterproduced}}{V_{waterproduced}} \\
\dfrac{{{V_{waterproduced}}}}{{{V_{ice}}}} = \dfrac{{{\rho _{ice}}}}{{{\rho _{waterproduced}}}}
\\
\]
Substituting the value of densities of water and ice, we get
\[\dfrac{{{V_{waterproduced}}}}{{{V_{ice}}}} = \dfrac{{0.917}}{1} = 0.917\]. As you can see that
\[\dfrac{{{V_{waterproduced}}}}{{{V_{ice}}}} < 1 \to {V_{waterproduced}} < {V_{ice}}\].
So, the volume that will be produced from the ice will be less than the actual volume of the ice. Now, if you consider the stone, it will not make a significant effect on the level of the water as the ice was already floating on the water. It will just sink down. Therefore, we can say that the water level will decrease after the ice has melted.
Therefore, both Assertion and Reason are correct and Reason is the correct explanation for
Assertion.
Thus,the correct option is (A).
Note:Always remember the values of the densities of water and ice, it will help you to solve many questions related to the ice water system. Also keep in mind the method we used to determine the volume produced from the melted ice, the mass will remain the same even after the change of state.