Consider two uniform discs of the same thickness and different radii <math> <msub> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mo>=</mo> <mi>R</mi> </math> and <math> <msub> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> <mo>=</mo> <mi>α</mi> <mi>R</mi> </math> made of the same material. If the ratio of their moments of inertia <math> <msub> <mrow> <mrow> <mi>I</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </math> and <math> <msub> <mrow> <mrow> <mi>I</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </math> , respectively, about their axes is <math> <msub> <mrow> <mrow> <mi>I</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mo>:</mo> <msub> <mrow> <mrow> <mi>I</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>:</mo> <mn>16</mn> </math> then the value of <math> <mi>α</mi> </math> is:

⇒ V 2 = U 2 + 2 g S ⇒ V 2 = 0 + 2 g ( h - y ) ⇒ V 2 = 2 g h - 2 g y ⇒ V = 2 g h - 2 g y

Consider two uniform discs of the same thickness and different radii <math> <msub> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mo>=</mo> <mi>R</mi> </math> and <math> <msub> <mrow> <mrow> <mi>R</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> <mo>=</mo> <mi>α</mi> <mi>R</mi> </math> made of the same material. If the ratio of their moments of inertia <math> <msub> <mrow> <mrow> <mi>I</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </math> and <math> <msub> <mrow> <mrow> <mi>I</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </math> , respectively, about their axes is <math> <msub> <mrow> <mrow> <mi>I</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> <mo>:</mo> <msub> <mrow> <mrow> <mi>I</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>:</mo> <mn>16</mn> </math> then the value of <math> <mi>α</mi> </math> is:

<math> <mn>2</mn> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> </math> (Rotational Mechanics)

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Physics Class 12th System of Particles and Rotational Motion Physics NCERT Exemplar Solutions Class 12th Chapter Seven

Consider two uniform discs of the same thickness and different radii $R_{1} = R$ and $R_{2} = α R$ made of the same material. If the ratio of their moments of inertia $I_{1}$ and $I_{2}$ , respectively, about their axes is $I_{1} : I_{2} = 1 : 16$ then the value of $α$ is:

Option 1 -

Option 2 -

$\sqrt[]{2}$

Option 3 -

Option 4 -

$2 \sqrt[]{2}$ (Rotational Mechanics)

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Answered by

alok kumar singh | Contributor-Level 10

3 months ago

Correct Option - 3

Detailed Solution:

$\begin{array}{r} \Rightarrow V^{2} = U^{2} + 2 g S \\ \Rightarrow V^{2} = 0 + 2 g (h - y) \\ \Rightarrow V^{2} = 2 g h - 2 g y \\ \Rightarrow V = \sqrt[]{2 g h - 2 g y} \end{array}$

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Consider two uniform discs of the same thickness and different radii $R_{1} = R$ and $R_{2} = α R$ made of the same material. If the ratio of their moments of inertia $I_{1}$ and $I_{2}$ , respectively, about their axes is $I_{1} : I_{2} = 1 : 16$ then the value of $α$ is:

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Consider two uniform discs of the same thickness and different radii R 1 = R and R 2 = α R made of the same material. If the ratio of their moments of inertia I 1 and I 2 , respectively, about their axes is I 1 : I 2 = 1 : 16 then the value of α is:

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Consider two uniform discs of the same thickness and different radii $R_{1} = R$ and $R_{2} = α R$ made of the same material. If the ratio of their moments of inertia $I_{1}$ and $I_{2}$ , respectively, about their axes is $I_{1} : I_{2} = 1 : 16$ then the value of $α$ is: