Question 232: Centre of Mass and Rotational Motion

Question

Three solid spheres each of mass m and
diameter d are stuck together such that the lines
connecting the centres form an equilateral
triangle of side of length d. The ratio I
0
/I
A
of
moment of inertia I
0
of the system about an axis
passing the centroid and about center of any
of the spheres I
A
and perpendicular to the plane
of the triangle is :

Accepted Answer

AB = d
$$ 	herefore $$ OA = $${{d \over {\sqrt 3 }}}$$
From parallel axis theorem
I
0
= $$3 	imes \left[ {{2 \over 5}M{{\left( {{d \over 2}} ight)}^2} + M{{\left( {{d \over {\sqrt 3 }}} ight)}^2}} ight]$$ = $${{13} \over {10}}M{d^2}$$
I
A
= I
0
+ 3M$${{{\left( {{d \over {\sqrt 3 }}} ight)}^2}}$$
= $${{13} \over {10}}M{d^2}$$ + Md
2
= $${{23} \over {10}}M{d^2}$$
$$ 	herefore $$ $${{{I_0}} \over {{I_A}}}$$ = $${{13} \over {23}}$$

Answer

$${{13} \over {23}}$$

Answer

$${{23} \over {13}}$$

Answer

$${{15} \over {13}}$$

Answer

$${{13} \over {15}}$$

Centre of Mass and Rotational Motion

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