Question 549: Centre of Mass and Rotational Motion

Question

Four identical uniform solid spheres each of same mass $$M$$ and radius $$R$$ are placed touching each other as shown in figure with centres $$A, B, C, D. I_A, I_B, I_C, I_D$$ are the moment of inertia of these spheres respectively about an axis passing through centre and perpendicular to the plane, then

Accepted Answer

The four identical uniform solid spheres are shown below. The radius of each sphere is $$R$$.
Lets take centre of the system at $$O$$.
Then, distance from the centre for $$r_B=r_C$$ and $$r_A=r_D$$
$$	herefore$$ Moment of inertial, $$M_0 I=M r^2$$, for each spheres will be $$I_A, I_B, I_C$$ and $$I_D$$.
$$\begin{array}{lll}
	herefore & I_A=I_D 	ext { and } I_B=I_C \
	ext { Since, } & r_B=r_C  I_B=I_C
\end{array}$$

Answer

$$I_A>I_B>I_C>I_D$$

Answer

$$I_D>I_C>I_B>I_A$$

Answer

$$I_A=I_D>I_B=I_C$$

Answer

$$I_A=I_D< I_B=I_C$$

Centre of Mass and Rotational Motion

Four identical uniform solid spheres each of same mass $M and radius R are placed touching each other as shown in figure with centres A, B, C, D. I_A, I_B, I_C, I_D$ are the moment of inertia of these spheres respectively about an axis passing through centre and perpendicular to the plane, then

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