A car is skidding on an icy road with speed  $v$ and tyres are rotating with angular speed $\frac{v}{3R}$ , where $R$  is the radius of tyres. The distance travelled by car in one rotation of tyres is

Correct Option - 4


Detailed Solution:

$\theta =\omega t$

$2\pi =\left(\frac{V}{3R}\right)T$

$?t=\frac{6\pi R}{V}$

The distance travelled by car in this time is

$s=vt$

$?s=v\left(\frac{6\pi R}{V}\right)$

$=6\pi R$

<div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1758175539phpcIhwKd.jpeg" alt="" width="285" height="261" loading="lazy"></picture></div></div><p><span contenteditable="false"> <math> <mi>θ</mi> <mo>=</mo> <mi>ω</mi> <mi>t</mi> </math> </span><br>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p><p><span contenteditable="false"> <math> <mn>2</mn> <mi>π</mi> <mo>=</mo> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mi>V</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> <mi>R</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> <mi>T</mi> </math> </span><br>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p><p><span contenteditable="false"> <math> <mo>? </mo> <mi>t</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>6</mn> <mi>π</mi> <mi>R</mi> </mrow> </mrow> <mrow> <mrow> <mi>V</mi> </mrow> </mrow> </mfrac> </math> </span></p><p>The distance travelled by car in this time is</p><p><span contenteditable="false"> <math> <mi>s</mi> <mo>=</mo> <mi>v</mi> <mi>t</mi> <mi> </mi> </math> </span><br>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p><p><span contenteditable="false"> <math> <mo>? </mo> <mi>s</mi> <mo>=</mo> <mi>v</mi> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>6</mn> <mi>π</mi> <mi>R</mi> </mrow> </mrow> <mrow> <mrow> <mi>V</mi> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </math> </span><br>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p><p><span contenteditable="false"> <math> <mo>=</mo> <mn>6</mn> <mi>π</mi> <mi>R</mi> </math> </span><br>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p>

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