If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is <math> <mrow> <mfrac> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> times its original time period. Then the value of <math> <mrow> <mi>x</mi> </mrow> </math> is:

T ′ = 2 π ? ′ g where t ′ = l 2   T = 2 π t g   T ′ = x 2 T   2 π t 2 g = x 2 2 π t g   1 2 = x 2 ⇒ x = 2

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is <math> <mrow> <mfrac> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> times its original time period. Then the value of <math> <mrow> <mi>x</mi> </mrow> </math> &nbsp;is:

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Physics Class 11th Physics Oscillations

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $\frac{x}{2}$ times its original time period. Then the value of $x$ is:

Option 1 -

$\sqrt[]{3}$

Option 2 -

$\sqrt[]{2}$

Option 3 -

$2 \sqrt[]{3}$

Option 4 -

2 Views | Posted a month ago

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 2

Detailed Solution:

$T^{'} = 2 π \sqrt[]{\frac{?^{'}}{g}}$ where $t^{'} = \frac{l}{2}$

$T = 2 π \sqrt[]{\frac{t}{g}}$

$T^{'} = \frac{x}{2} T$

$2 π \sqrt[]{\frac{t}{2 g}} = \frac{x}{2} 2 π \sqrt[]{\frac{t}{g}}$

$\frac{1}{\sqrt[]{2}} = \frac{x}{2} \Rightarrow x = \sqrt[]{2}$

<math> <mrow> <msup> <mi>T</mi> <mo>′</mo> </msup> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mroot> <mrow> <mfrac> <mrow> <msup> <mi>? </mi> <mo>′</mo> </msup> </mrow> <mrow> <mi>g</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math> where <math> <mrow> <msup> <mi>t</mi> <mo>′</mo> </msup> <mo>=</mo> <mfrac> <mrow> <mi mathvariant="script">l</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math>   <math> <mrow> <mi>T</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mroot> <mrow> <mfrac> <mrow> <mi>t</mi> </mrow> <mrow> <mi>g</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math>   <math> <mrow> <msup> <mi>T</mi> <mo>′</mo> </msup> <mo>=</mo> <mfrac> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mi>T</mi> </mrow> </math>   <math> <mrow> <mn>2</mn> <mi>π</mi> <mroot> <mrow> <mfrac> <mrow> <mi>t</mi> </mrow> <mrow> <mn>2</mn> <mi>g</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> <mo>=</mo> <mfrac> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mn>2</mn> <mi>π</mi> <mroot> <mrow> <mfrac> <mrow> <mi>t</mi> </mrow> <mrow> <mi>g</mi> </mrow> </mfrac> </mrow> <mrow></mrow> </mroot> </mrow> </math>   <math> <mrow> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mo>⇒</mo> <mi>x</mi> <mo>=</mo> <mroot> <mrow> <mn>2</mn> </mrow> <mrow></mrow> </mroot> </mrow> </math>

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If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $\frac{x}{2}$ times its original time period. Then the value of $x$ is:

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If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x 2 times its original time period. Then the value of x is:

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If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $\frac{x}{2}$ times its original time period. Then the value of $x$ is: