A curved in a level road has  aradius 75m. The maximum speed of a car turning this curved road can be 30 m/s without skidding.; If radius of curved road is changed to 48m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be…….m/s.

$f=\frac{m{v}^2}{R}$            

$\Rightarrow \frac{m{v}^2}{R}=\mu N$

 

$\frac{m{v}^2}{R}=\mu mg$

$\Rightarrow 30=\sqrt[]{\mu \times 75\times 10}$                

  $\mu =\frac{30\times 30}{750}=1.2$              

              Now, R = 48 m (new Radius of curvature)

    $\mu =1.2$

$V_{max}=\sqrt[]{\mu Rg}$

$=\sqrt[]{1.2\times 48\times 10}$            

$=24m/sec$               

 

<p><span contenteditable="false"> <math><mrow><mi>f</mi><mo>=</mo><mfrac><mrow><mi>m</mi><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mi>R</mi></mrow></mfrac></mrow></math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p><div><div><picture><source srcset="" media="(max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1753954827phpfH4SJn.jpeg" alt="" width="326" height="157" loading="lazy"></picture></div><div><span contenteditable="false"> <math> <mrow> <mo>⇒</mo> <mfrac> <mrow> <mi>m</mi> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>R</mi> </mrow> </mfrac> <mo>=</mo> <mi>μ</mi> <mi>N</mi> </mrow> </math> </span></div><div>&nbsp;</div></div><p><span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mi>m</mi> <msup> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>R</mi> </mrow> </mfrac> <mo>=</mo> <mi>μ</mi> <mi>m</mi> <mi>g</mi> </mrow> </math> </span></p><p><span contenteditable="false"> <math> <mrow> <mo>⇒</mo> <mn>3</mn> <mn>0</mn> <mo>=</mo> <mroot> <mrow> <mi>μ</mi> <mo>×</mo> <mn>7</mn> <mn>5</mn> <mo>×</mo> <mn>1</mn> <mn>0</mn> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1815480382"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;&nbsp;</p><p>&nbsp;<span contenteditable="false"> <math> <mrow> <mi>μ</mi> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> <mn>0</mn> <mo>×</mo> <mn>3</mn> <mn>0</mn> </mrow> <mrow> <mn>7</mn> <mn>5</mn> <mn>0</mn> </mrow> </mfrac> <mo>=</mo> <mn>1</mn> <mo>.</mo> <mn>2</mn> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1815480383"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;&nbsp;</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Now, R = 48 m (new Radius of curvature)</p><p>&nbsp; &nbsp;<span contenteditable="false"> <math> <mrow> <mi>μ</mi> <mo>=</mo> <mn>1</mn> <mo>.</mo> <mn>2</mn> </mrow> </math> </span></p><p><span contenteditable="false"> <math> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mroot> <mrow> <mi>μ</mi> <mi>R</mi> <mi>g</mi> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p><p><span contenteditable="false"> <math> <mrow> <mo>=</mo> <mroot> <mrow> <mn>1</mn> <mo>.</mo> <mn>2</mn> <mo>×</mo> <mn>4</mn> <mn>8</mn> <mo>×</mo> <mn>1</mn> <mn>0</mn> </mrow> <mrow></mrow> </mroot> </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_i1030" DrawAspect="Content" ObjectID="_1815480384"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;&nbsp;</p><p><span contenteditable="false"> <math> <mrow> <mo>=</mo> <mn>2</mn> <mn>4</mn> <mi>m</mi> <mo>/</mo> <mi>s</mi> <mi>e</mi> <mi>c</mi> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1031" DrawAspect="Content" ObjectID="_1815480385"> </o:OLEObject>&lt;/xml&gt;&lt;![endif]--&gt;&nbsp;</p><p>&nbsp;</p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment