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can u plz give me the answer of this question ? rotation motion – question no 3 --there are four solid balls....

can u plz give me the answer of this question ?
rotation motion –  question no 3 --there are four solid balls....

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Grade:12th pass

1 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
The moment of inertia of the balls about axes passing rhough their centers is
$$I=\dfrac{2}{5}mr^2$$
(i) The moment of inertia of two balls through whose centers the side of the square passes is
$$I_1=I_2=\dfrac{2}{5}mr^2$
From parallel axis theorem, the moment of inertia of the two other balls about the same axis is
I_3=I_4=\dfrac{2}{5}mr^2+ma^2

Hence the total moment of inertia=\dfrac{8}{5}mr^2+2ma^2

(ii) Distance OA=\dfrac{a}{\sqrt{2}}

Moment of inertia of two balls passing thorugh the diagonal axis considered=\dfrac{2}{5}mr^2each

Moment of inertia of the other two balls is
\dfrac{2}{5}mr^2+m(OA)^2
=\dfrac{2}{5}mr^2+m\dfrac{a^2}{2} each

Hence the total moment of inertia=\dfrac{8}{5}mr^2+ma^2

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