Question

If the radius of solid sphere is doubled by keeping its mass constant, compare the moment of inertia about any diameter. (Ans.: 1:4)

Answer 1

Answer:

$I\ :\ I'\ =\ 1\ :\ 4$

Explanation:

Let R be the radius and M be the mass of the solid sphere,

Therefore,  moment of inertia = I = $\dfrac{2}{5}MR^2$

Now the radius of the new sphere is doubled, therefore the radius of the new sphere is 2R

Now the moment of inertia of the new sphere = $I'\ =\ \dfrac{2}{5}M(2R)^2\ =\ 4\times \dfrac{2}{5}MR^2\ =\ 4\ I$

Comparision between the initial and new sphere,

$I\ :\ I'\ =\ 1\ :\ 4$

Answer 2

Answer in attachment

Explanation:

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