Physics Oscillations Class 11th Physics

A solid cylinder attached to horizontal massless spring can roll without slipping along horizontal surface. Find time period of oscillation.

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>2</mn> <mi>π</mi> <mroot> <mrow> <mfrac> <mrow> <mi>M</mi> </mrow> <mrow> <mn>2</mn> <mi>k</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>π</mi> <mroot> <mrow> <mfrac> <mrow> <mn>3</mn> <mi>M</mi> </mrow> <mrow> <mn>2</mn> <mi>k</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>π</mi> <mroot> <mrow> <mfrac> <mrow> <mn>2</mn> <mi>M</mi> </mrow> <mrow> <mn>3</mn> <mi>k</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mn>2</mn> <mi>π</mi> <mroot> <mrow> <mfrac> <mrow> <mn>3</mn> <mi>M</mi> </mrow> <mrow> <mn>2</mn> <mi>k</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>

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Alok Kumar Singh | Contributor-Level 10

5 months ago

Correct Option - 4

Detailed Solution:

$τ_{A} = I α$

$K x R = \frac{3}{2} M R^{2} α$

$K R θ R = \frac{3}{2} M R^{2} α$

$α = \frac{2 K}{3 M}$

$∴ T = 2 π \sqrt[]{\frac{3 M}{2 K}}$

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