Question 231: 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 :
![](https://imagex.cdn.examgoal.net/7k9k2k5imvulf/cc0f90ad-e97b-4d41-8dca-9bf3173e97c3/8375bf30-396a-11ea-92dd-4b9c3519996f/file-7k9k2k5imvulg-411w.jpg)

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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