Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged if the density of ice is $\rho$ _i = 0.917 g cm^-3 ?

<p><span data-teams="true">This is a short answer type question as classified in NCERT Exemplar</span></p><p>Given density of ice <span contenteditable="false"> <math> <mi mathvariant="bold-italic">ρ</mi> </math> </span>_i = 0.917 g cm^-3</p><p>Density of water <span contenteditable="false"> <math> <msub> <mrow> <mrow> <mi>ρ</mi> </mrow> </mrow> <mrow> <mrow> <mi>w</mi> </mrow> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mi>g</mi> <mo>/</mo> <mi>c</mi> <mi>m</mi> </math> </span>³</p><p>Let V be the total volume of iceberg and V’ of its volume be submerged in water.</p><p>In floating condition</p><p>Weight of the iceberg= weight of the water displaced by the submerged part by ice</p><p>V <span contenteditable="false"> <math> <mi>ρ</mi> </math> </span>_ig = V’<span contenteditable="false"> <math> <msub> <mrow> <mrow> <mi>ρ</mi> </mrow> </mrow> <mrow> <mrow> <mi>w</mi> </mrow> </mrow> </msub> </math> </span>g</p><p><span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>V</mi> <mi>'</mi> </mrow> </mrow> <mrow> <mrow> <mi>V</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>ρ</mi> </mrow> </mrow> <mrow> <mrow> <mi>i</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>ρ</mi> </mrow> </mrow> <mrow> <mrow> <mi>w</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> </math> </span>=<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>0.917</mn> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>0.917</mn> </math> </span></p>

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