Class 11th Torque and Angular Momentum Physics System of Particles and Rotational Motion Physics

A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads^-1 in a horizontal plane about an axis vertical to its plane and passing through the centre of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of ring, the will then rotate with an angular velocity (in rads^-¹).

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mi>M</mi> </mrow> <mrow> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>+</mo> <mi>m</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>+</mo> <mn>2</mn> <mi>m</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>2</mn> <mi>M</mi> </mrow> </mfrac> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>2</mn> <mi>M</mi> </mrow> <mrow> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>+</mo> <mn>2</mn> <mi>m</mi> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <mi>M</mi> <mo>+</mo> <mn>2</mn> <mi>m</mi> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>M</mi> </mrow> </mfrac> </mrow> </math> </span></p>

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Answered by

Raj Pandey | Contributor-Level 9

4 months ago

Correct Option - 3

Detailed Solution:

By conservation of Angular momentum

Li = Lf

$M R^{2} ω = (m R^{2} + 2 m R^{2}) ω'$

$\frac{2 M}{M + 2 m} = ω'$

$\Rightarrow$ $ω' = \frac{2 M}{M + 2 m}$

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Physics System of Particles and Rotational Motion 2025

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