First slide

Moment of intertia

Question

If 27 small spheres each of M.I. ‘I’ about their diametrical axis are combined to form a big sphere, then the M.I. of the big sphere about its diameter is

Moderate

A

243 I
B

81 I
C

27 I
D

9 I

Solution

$\large {I_1} = \frac{2}{5}m{r^2};\;\frac{4}{3}\pi {R^3} = 27\frac{4}{3}\pi {r^3} \Rightarrow R = 3r$

MI of big sphere

$\large {I{}'} = \frac{2}{5}\left( {27m} \right){R^2} = \frac{2}{5}\left( {27m} \right)9{r^2}$

$\large {I{}'} = \243 I$

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