A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is v in the direction shown, which one of the following options is correct ( P and Q  are any highest and lowest points on the wheel, respectively)?

 

Option 1 - <p><span lang="EN-IN">Point <span class="mathml" contenteditable="false"> <math> <mrow> <mi>P</mi> </mrow> </math> </span>moves slower than point <span class="mathml" contenteditable="false"> <math> <mrow> <mi>Q</mi> </mrow> </math> </span>&lt;!--[endif]--&gt;&lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1816431498"> </o:OLEObject> &lt;/xml&gt;&lt;![endif]--&gt;</span></p>
Option 2 - <p><span lang="EN-IN">Point <span class="mathml" contenteditable="false"> <math> <mrow> <mi>P</mi> </mrow> </math> </span> moves faster than point <span class="mathml" contenteditable="false"> <math> <mrow> <mi>Q</mi> </mrow> </math> </span>&lt;!--[endif]--&gt;&lt;!-- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1816431505"> </o:OLEObject> &lt;/xml&gt;&lt;![endif]--&gt;</span></p>
Option 3 - <p><span lang="EN-IN">Both the points <span class="mathml" contenteditable="false"> <math> <mrow> <mi>P</mi> </mrow> </math> </span>&nbsp;and <span class="mathml" contenteditable="false"> <math> <mrow> <mi>Q</mi> </mrow> </math> </span>&nbsp;move with equal speed</span></p>
Option 4 - <p><span lang="EN-IN">Point <span class="mathml" contenteditable="false"> <math> <mrow> <mi>P</mi> </mrow> </math> </span>&lt;!-- [if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"/> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"/> <v:f eqn="sum @0 1 0"/> <v:f eqn="sum 0 0 @1"/> <v:f eqn="prod @2 1 2"/> <v:f eqn="prod @3 21600 pixelWidth"/> <v:f eqn="prod @3 21600 pixelHeight"/> <v:f eqn="sum @0 0 1"/> <v:f eqn="prod @6 1 2"/> <v:f eqn="prod @7 21600 pixelWidth"/> <v:f eqn="sum @8 21600 0"/> <v:f eqn="prod @7 21600 pixelHeight"/> <v:f eqn="sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> <o:lock v:ext="edit" aspectratio="t"/> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style='width:13pt;\\\\\\\\n height:13.5pt' o:ole=""> <v:imagedata src="file:///C:/Users/ALOK~1.SIN/AppData/Local/Temp/msohtmlclip1/01/clip_image001.wmz" o:title=""/> </v:shape><![endif]--&gt;&lt;!-- [if !vml]--&gt;has zero speed</span></p>
17 Views|Posted 5 months ago
Asked by Shiksha User
1 Answer
A
5 months ago
Correct Option - 4
Detailed Solution:

In the case of pure rolling,

The topmost point will have velocity 2 v while point Q i.e. the lowest point will have zero velocity. Hence point P moves faster than point Q .

 

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