First slide

Moment of intertia

Question

A solid aluminium sphere of radius R has moment of inertia l about an axis through its centre. The moment of inertia about a central axis of a solid aluminium sphere of radius 2R is

Easy

A

4I
B

8I
C

16I
D

32I

Solution

I = $\frac{2}{5} M^{} R^{2} = \frac{2}{5} (\frac{4}{3} {πR}^{3} ρ) R^{2} \Rightarrow I \infty R^{5} \frac{I^{,}}{I} = {(\frac{2 R}{R})}^{5} = 32 \Rightarrow I^{,} = 32 I$

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