A leak proof cylinder of length $1\mathrm{m}$ $$ , made of a metal which has very low coefficient of expansion is floating vertically in water at $0^{?}\mathrm{C}$ ${}^{}$ such that its height above the water surface is $20\mathrm{c}\mathrm{m}$ $$ . When the temperature of water is increased to $4^{?}\mathrm{C}$ ${}^{}$ , the height of the cylinder above the water surface becomes $$ $21\mathrm{c}\mathrm{m}$ . The density of water at $\mathrm{T}=4^{?}\mathrm{C}$ ${}^{}$ , relative to the density at $\mathrm{T}=0^{?}\mathrm{C}$ ${}^{}$ is close to:

Correct Option - 1


Detailed Solution:

$\begin{array}{rr}& \mathrm{m}\mathrm{g}=\mathrm{A}\left(80\right){\rho }_{0^{?}\mathrm{C}}\mathrm{g}\\ & \mathrm{m}\mathrm{g}=\mathrm{A}\left(79\right){\rho }_{4^{?}\mathrm{C}}\mathrm{g}\\ & \frac{{\rho }_{4^{?}\mathrm{C}}}{{\rho }_{0^{?}\mathrm{C}}}=\frac{80}{79}=1.01\end{array}$

 

<div class="photo-widget-full"><div class="figure"><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1755770065phpOpFHYT.jpeg" alt="" width="224" height="107" loading="lazy"></picture></div></div><p><span contenteditable="false"> <math> <mtable columnalign="right"> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">g</mi> <mo>=</mo> <mi mathvariant="normal">A</mi> <mo> (</mo> <mn>80</mn> <mo>)</mo> <msub> <mrow> <mrow> <mi>ρ</mi> </mrow> </mrow> <mrow> <mrow> <msup> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> <mrow> <mrow> <mo>? </mo> </mrow> </mrow> </msup> <mi mathvariant="normal">C</mi> </mrow> </mrow> </msub> <mi mathvariant="normal">g</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">g</mi> <mo>=</mo> <mi mathvariant="normal">A</mi> <mo> (</mo> <mn>79</mn> <mo>)</mo> <msub> <mrow> <mrow> <mi>ρ</mi> </mrow> </mrow> <mrow> <mrow> <msup> <mrow> <mrow> <mn>4</mn> </mrow> </mrow> <mrow> <mrow> <mo>? </mo> </mrow> </mrow> </msup> <mi mathvariant="normal">C</mi> </mrow> </mrow> </msub> <mi mathvariant="normal">g</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>ρ</mi> </mrow> </mrow> <mrow> <mrow> <msup> <mrow> <mrow> <mn>4</mn> </mrow> </mrow> <mrow> <mrow> <mo>? </mo> </mrow> </mrow> </msup> <mi mathvariant="normal">C</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>ρ</mi> </mrow> </mrow> <mrow> <mrow> <msup> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> <mrow> <mrow> <mo>? </mo> </mrow> </mrow> </msup> <mi mathvariant="normal">C</mi> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>80</mn> </mrow> </mrow> <mrow> <mrow> <mn>79</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>1.01</mn> </mrow> </mtd> </mtr> </mtable> </math> </span></p><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1755770125phpiqZt6A.jpeg" alt="" width="309" height="162" loading="lazy"></picture></div></div><p>&nbsp;</p></div></div>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment