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  • There is a metal cube inside a block of ice which is floating on the surface of water. The ice melts completely and metal falls in the water. Water level in the container <img alt="" src=

There is a metal cube inside a block of ice which is floating on the surface of water. The ice melts completely and metal falls in the water. Water level in the container

Option: 1

Rises
 


Option: 2

Falls
 


Option: 3

Remains same
 


Option: 4

Nothing can be concluded


Answers (1)

best_answer

Initially

\mathrm{ \begin{aligned} & \mathrm{W}_{\text {metal }}=\mathrm{W}_{\text {ice }}=\text { Buoyancy } \\\\ & \mathrm{V}_{\text {metal }} \rho \mathrm{mg}+\mathrm{V}_{\text {ice }} \rho_{\text {ice }} \mathrm{g}=\mathrm{V}_{\mathrm{d}} \rho_{\ell} \mathrm{g} \\\\ & \therefore \mathrm{V}_{\mathrm{d}}=\frac{\mathrm{V}_{\text {metal }} \rho_{\mathrm{m}}}{\rho_{\ell}}+\frac{\mathrm{V}_{\text {ice }} \rho_{\text {ice }}}{\rho_{\ell}} \end{aligned} }
finally volume displaced

\mathrm{ \begin{array}{ll} \mathrm{V}=\mathrm{V}_{\mathrm{m}}+\mathrm{V}_{\mathrm{w}} \text { (From ice) } & \\\\ =\mathrm{V}_{\mathrm{m}}+\frac{\mathrm{m}}{\rho_{\mathrm{w}}} \quad=\mathrm{V}_{\mathrm{m}}+\frac{\mathrm{V}_{\mathrm{i}} \ell_{\mathrm{i}}}{\rho_{\mathrm{w}}}<\text { previous } \end{array} }

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Pankaj

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