Two springs with spring constants <math> <msub> <mrow> <mrow> <mi>k</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mo>=</mo> <mn>1200</mn> <mi> </mi> <mi>N</mi> <mo>/</mo> <mi>m</mi> </math> and <math> <msub> <mrow> <mrow> <mi>k</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> <mo>=</mo> <mn>500</mn> <mi> </mi> <mi>N</mi> <mo>/</mo> <mi>m</mi> </math> are stretched by the same force. The ratio of potential energy in the springs will be

Elastic potential energy stored in the spring U = 1 2 k x 2 = 1 2 F x = F 2 2 k H e n c e U 1 U 2 = k 2 k 1 F i s s a m e f o r b o t h s p r i n g s = 500 1200 = 5 12

Two springs with spring constants <math> <msub> <mrow> <mrow> <mi>k</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mo>=</mo> <mn>1200</mn> <mi> </mi> <mi>N</mi> <mo>/</mo> <mi>m</mi> </math> and <math> <msub> <mrow> <mrow> <mi>k</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> <mo>=</mo> <mn>500</mn> <mi> </mi> <mi>N</mi> <mo>/</mo> <mi>m</mi> </math> are stretched by the same force. The ratio of potential energy in the springs will be

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Physics Class 11th Work, Energy and Power

Two springs with spring constants $k_{1} = 1200 N / m$ and $k_{2} = 500 N / m$ are stretched by the same force. The ratio of potential energy in the springs will be

Option 1 -

$\frac{25}{144}$

Option 2 -

$\frac{2 Q E}{k}$

Option 3 -

$\frac{Q E}{2 k}$

Option 4 -

$\frac{3 Q E}{2 k}$

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

2 weeks ago

Correct Option - 3

Detailed Solution:

Elastic potential energy stored in the spring

$U = \frac{1}{2} k x^{2}$

$= \frac{1}{2} F x = \frac{F^{2}}{2 k}$

$H e n c e \frac{U_{1}}{U_{2}} = \frac{k_{2}}{k_{1}} [F i s s a m e f o r b o t h s p r i n g s]$

$= \frac{500}{1200} = \frac{5}{12}$

Elastic potential energy stored in the spring <math> <mi>U</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mi>k</mi> <msup> <mrow> <mrow> <mi>x</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </math> <math> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> <mi>F</mi> <mi>x</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <msup> <mrow> <mrow> <mi>F</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> <mi>k</mi> </mrow> </mrow> </mfrac> </math> <math> <mi>H</mi> <mi>e</mi> <mi>n</mi> <mi>c</mi> <mi>e</mi> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>U</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>U</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>k</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <msub> <mrow> <mrow> <mi>k</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </mrow> </mrow> </mfrac> <mi> </mi> <mfenced open=" [" close="]" separators="|"> <mrow> <mrow> <mi> </mi> <mi>F</mi> <mi> </mi> <mi>i</mi> <mi>s</mi> <mi> </mi> <mi>s</mi> <mi>a</mi> <mi>m</mi> <mi>e</mi> <mi> </mi> <mi>f</mi> <mi>o</mi> <mi>r</mi> <mi> </mi> <mi>b</mi> <mi>o</mi> <mi>t</mi> <mi>h</mi> <mi> </mi> <mi>s</mi> <mi>p</mi> <mi>r</mi> <mi>i</mi> <mi>n</mi> <mi>g</mi> <mi>s</mi> </mrow> </mrow> </mfenced> </math> <math> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>500</mn> </mrow> </mrow> <mrow> <mrow> <mn>1200</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> <mrow> <mrow> <mn>12</mn> </mrow> </mrow> </mfrac> </math>

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Two springs with spring constants $k_{1} = 1200 N / m$ and $k_{2} = 500 N / m$ are stretched by the same force. The ratio of potential energy in the springs will be

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Two springs with spring constants $k_{1} = 1200 N / m$ and $k_{2} = 500 N / m$ are stretched by the same force. The ratio of potential energy in the springs will be