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JEE Main 20204 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
4 September
Shift
Evening Shift
Subject
Physics
Chapter
Rotational Motion

JEE Main 2020 · 4 September · Evening Shift · Physics · Rotational Motion

Consider two uniform discs of the same thickness and different...

Consider two uniform discs of the same thickness and different radii R1=R{R}_{1} = R and R2=\alphaR{R}_{2} = \alphaR made of the same material. If the ratio of their moments of inertia I1{I}_{1} and I2{I}_{2}, respectively, about their axes is I1:I2=1:16{I}_{1}: {I}_{2} = 1: 16 then the value of α\alpha is :

Options

  1. A222\sqrt{2}
  2. B2\sqrt{2}
  3. C22
  4. D44

Correct answer

C. 22

Step-by-step solution

Moment of inertia of disc is given by I=MR22=[ρ(πR2)t]R22I = \dfrac{{MR}^{2}}{2} = \dfrac{\left[ρ\left({\pi R}^{2}\right)t\right]{R}^{2}}{2}

IαR4I\alpha{R}^{4}

I2I1=(R2R1)4\dfrac{{I}_{2}}{{I}_{1}} = {\left(\dfrac{{R}_{2}}{{R}_{1}}\right)}^{4}

161=α4\dfrac{16}{1} = {\alpha}^{4}

α=2\alpha = 2

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