Consider two uniform discs of the same thickness and different radii R_1=R and R_2= αR made of the same material. If the ratio of their moments of inertia I_1 and I_2, respectively, about their axes…

Question

Consider two uniform discs of the same thickness and different radii R_1=R and R_2= αR 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 is:

Accepted Answer

Correct answer: A. (a) Moment of Inertia, I ∝ mR^2 ⇒I ∝ σπR^2 tR^2 [ Thickness and material is same ] ⇒I ∝R^4 ∴ R_2R_1= I_2I_1^1/4= (16 )^1/4=2 ⇒ =2

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

Solution

More Rotational Mechanics PYQs