A uniform chain of 6m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from the table is………….m.

F.B.D. of hanging length

F.B.D. of chain lying on the table

f = T = $\mu N$  

$\Rightarrow \lambda xg=\mu \lambda \left(L-x\right)g$  

$x=0.5\left(6-x\right)$  

$\Rightarrow x=3-0.5x$    

  $1.5x=3$  

x = 2m

 

<p>F.B.D. of hanging length</p><p>F.B.D. of chain lying on the table</p><p>f = T =<span contenteditable="false"> <math> <mrow> <mi>μ</mi> <mi>N</mi> </mrow> </math> </span>&nbsp;</p><p><span contenteditable="false"> <math> <mrow> <mo>⇒</mo> <mi>λ</mi> <mi>x</mi> <mi>g</mi> <mo>=</mo> <mi>μ</mi> <mi>λ</mi> <mrow> <mo> (</mo> <mrow> <mi>L</mi> <mo>−</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> <mi>g</mi> </mrow> </math> </span>&nbsp;</p><p><span contenteditable="false"> <math> <mrow> <mi>x</mi> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>5</mn> <mrow> <mo> (</mo> <mrow> <mn>6</mn> <mo>−</mo> <mi>x</mi> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span>&nbsp;</p><p><span contenteditable="false"> <math> <mrow> <mo>⇒</mo> <mi>x</mi> <mo>=</mo> <mn>3</mn> <mo>−</mo> <mn>0</mn> <mo>.</mo> <mn>5</mn> <mi>x</mi> </mrow> </math> </span>&nbsp; &nbsp;</p><p>&nbsp;<span contenteditable="false"> <math> <mrow> <mn>1</mn> <mo>.</mo> <mn>5</mn> <mi>x</mi> <mo>=</mo> <mn>3</mn> </mrow> </math> </span> &nbsp;</p><p>x = 2m</p><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1757396465phpWc1fAd.jpeg" alt="" width="172" height="173" loading="lazy"></picture></div></div><p>&nbsp;</p>

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