Rotational Motion

JEE Main level, single correct, medium

67 of 280

Question 67 of 280

Consider two uniform discs of the same thickness and different radii R1=R{R}_{1}=R and R2=αR{R}_{2}=\alpha R 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 :

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Answer: (C) 22

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