Physics Mechanical Properties of Fluids Class 11th Physics

Two blocks of same mass but different density $ρ_{1} & ρ_{2}$ are floating in water. Block-2 has higher fraction of its volume submerged in water. If buoyant force on them are B₁ & B₂ :-

Option 1 - <p>B<sub>1</sub> > B<sub>2</sub>, <span class="mathml" contenteditable="false"> <math> <mrow> <msub> <mrow> <mi>ρ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>></mo> <msub> <mrow> <mi>ρ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </math> </span> </p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <msub> <mrow> <mi>B</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo><</mo> <msub> <mrow> <mi>B</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>ρ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo><</mo> <msub> <mrow> <mi>ρ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <msub> <mrow> <mi>B</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mi>B</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>ρ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>></mo> <msub> <mrow> <mi>ρ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <msub> <mrow> <mi>B</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mi>B</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>ρ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo><</mo> <msub> <mrow> <mi>ρ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </math> </span></p>

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Answered by

Vishal Baghel | Contributor-Level 10

a month ago

Correct Option - 4

Detailed Solution:

$B = m g \Rightarrow B_{1} = B_{2}$

$ρ_{1} V_{1} g = B = ρ_{w} v_{L D} g$

$\frac{ρ_{2}}{ρ_{W}} = f_{2}$

$\Rightarrow ρ_{1} > ρ_{1}$

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