An inclined plane in bent in such a way that the vertical cross-section is given by y $=\frac{x^2}{4}$  where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $\mu$ = 0.5, the maximum height in cm at with a stationary block with not skip downward is ____________cm.

If the block does not slide,

mg sin    $\theta \le \mu mgcos\theta$

  $\Rightarrow tan\theta \le \mu \Rightarrow \frac{dy}{dx}\le \mu \Rightarrow \frac{x}{2}\le 0.5\Rightarrow x\le 1m.$         

 Thus, $y\le \frac{1^2}{4}=0.25m=25cm.$  

 

<p>If the block does not slide, </p><p>mg sin&nbsp;&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1818927447"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;&nbsp;<span contenteditable="false"> <math> <mrow> <mi>θ</mi> <mo>≤</mo> <mi>μ</mi> <mtext> </mtext> <mtext> </mtext> <mi>m</mi> <mi>g</mi> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>θ</mi> </mrow> </math> </span></p><p>&nbsp; <span contenteditable="false"> <math> <mrow> <mo>⇒</mo> <mi>t</mi> <mi>a</mi> <mi>n</mi> <mi>θ</mi> <mo>≤</mo> <mi>μ</mi> <mo>⇒</mo> <mfrac> <mrow> <mi>d</mi> <mi>y</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> <mo>≤</mo> <mi>μ</mi> <mo>⇒</mo> <mfrac> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mo>≤</mo> <mn>0</mn> <mo>.</mo> <mn>5</mn> <mo>⇒</mo> <mi>x</mi> <mo>≤</mo> <mn>1</mn> <mi>m</mi> <mo>.</mo> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1818927448"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;</p><p>&nbsp;Thus, <span contenteditable="false"> <math> <mrow> <mi>y</mi> <mo>≤</mo> <mfrac> <mrow> <msup> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>2</mn> <mn>5</mn> <mi>m</mi> <mo>=</mo> <mn>2</mn> <mn>5</mn> <mi>c</mi> <mi>m</mi> <mo>.</mo> </mrow> </math> </span>&nbsp;&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1818927449"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;</p><div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1757402018phpYRf4Gz.jpeg" alt="" width="354" height="213" loading="lazy"></picture></div></div><p>&nbsp;</p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment