A uniform disc with mass M = 4 kg and radius R = 10 cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m = 2kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is_________ N.

 

NLM² for (1)                                   

mg – T = ma

Þ 2 × 10 – T = 2a

Þ T + 2a = 20                   - (1)

Rotation equestion for (2)

T × R = I_cma

Þ T R =  $I_{CM}\frac{a}{R}$

  $\left[\alpha =\frac{a}{R},Noslippingcondition\right]$

T = $\frac{Ma}{2}$  

$T=\frac{4}{2}a$

T = 2a                  - (2)

from (1) & (2)

2T = 20

T = 10N

 

<p>NLM² for (1)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</p><p>mg – T = ma</p><p>Þ 2 × 10 – T = 2a</p><p>Þ T + 2a = 20 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; - (1)</p><p>Rotation equestion for (2)</p><p>T × R = I_cma</p><p>Þ T R =&nbsp;&lt;!--- [if gte mso 9]--&gt; &lt;!-- [endif]---&gt; <span contenteditable="false"> <math> <mrow> <msub> <mrow> <mi>I</mi> </mrow> <mrow> <mi>C</mi> <mi>M</mi> </mrow> </msub> <mfrac> <mrow> <mi>a</mi> </mrow> <mrow> <mi>R</mi> </mrow> </mfrac> </mrow> </math> </span></p><p>&nbsp;<span contenteditable="false"> <math> <mrow> <mrow> <mo> [</mo> <mrow> <mi>α</mi> <mo>=</mo> <mfrac> <mrow> <mi>a</mi> </mrow> <mrow> <mi>R</mi> </mrow> </mfrac> <mo>, </mo> <mi>N</mi> <mi>o</mi> <mtext> </mtext> <mtext> </mtext> <mi>s</mi> <mi>l</mi> <mi>i</mi> <mi>p</mi> <mi>p</mi> <mi>i</mi> <mi>n</mi> <mi>g</mi> <mtext> </mtext> <mtext> </mtext> <mi>c</mi> <mi>o</mi> <mi>n</mi> <mi>d</mi> <mi>i</mi> <mi>t</mi> <mi>i</mi> <mi>o</mi> <mi>n</mi> </mrow> <mo>]</mo> </mrow> </mrow> </math> </span></p><p>T = <span contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mi>M</mi> <mi>a</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> </span>&lt;!--- [if gte mso 9]--&gt; &lt;!-- [endif]---&gt;&nbsp;</p><p><span contenteditable="false"> <math> <mrow> <mi>T</mi> <mo>=</mo> <mfrac> <mrow> <mn>4</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mi>a</mi> </mrow> </math> </span></p><p>T = 2a&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; - (2)</p><p>from (1) &amp; (2)</p><p>2T = 20</p><p>T = 10N</p><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media="(max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1753069556phpOILUUP.jpeg" alt="" width="360" height="272" loading="lazy"></picture></div></div><p>&nbsp;</p>

0 Upvotes 0 Upvotes 0 Downvotes

• • Report Abuse
• Comment