Class 11th Laws of Motion Physics Physics Laws of Motion

A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $ω .$ The coefficient of static friction between the bottom of the beaker and the surface of the disc is $μ$ . The beaker will revolve with the disc if :

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>R</mi> <mo>≤</mo> <mfrac> <mrow> <mi>μ</mi> <mi>g</mi> </mrow> <mrow> <mn>2</mn> <msup> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>R</mi> <mo>≤</mo> <mfrac> <mrow> <mi>μ</mi> <mi>g</mi> </mrow> <mrow> <msup> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>R</mi> <mo>≥</mo> <mfrac> <mrow> <mi>μ</mi> <mi>g</mi> </mrow> <mrow> <mn>2</mn> <msup> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>R</mi> <mo>≥</mo> <mfrac> <mrow> <mi>μ</mi> <mi>g</mi> </mrow> <mrow> <msup> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </math> </span></p>

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Alok Kumar Singh | Contributor-Level 10

7 months ago

Correct Option - 2

Detailed Solution:

F. B. D of Beaker

By NLM2

$\begin{array}{l} f = m a = m ω^{2} R \\ \Rightarrow m ω^{2} R \leq μ N \\ R \leq μ g / ω^{2} \end{array}$

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