Physics Oscillations Class 11th Physics

If two similar spring each of spring constant K₁ are joined in series, the new spring constant and time period would be changed by a factor

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mo>,</mo> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mo>,</mo> <mn>2</mn> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> <mo>,</mo> <mn>2</mn> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> <mo>,</mo> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span></p>

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Payal Gupta | Contributor-Level 10

6 months ago

Correct Option - 1

Detailed Solution:

T $1 = 2 π \sqrt[]{\frac{m}{k}}$

$k_{e q} = \frac{k * k}{k + k} = \frac{k}{2}$

$T_{2} = 2 π \sqrt[]{\frac{m}{(k / 2)}} = 2 π \sqrt[]{\frac{2 m}{k}}$

$\Rightarrow \frac{T_{2}}{T_{1}} = \sqrt[]{2} a n d \frac{k_{2}}{k_{1}} = \frac{1}{2}$

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