First slide

Moment of intertia

Question

What is the moment of inertia of solid sphere of density $ρ$ and radius R about its diameter? [UP CPMT 2012]

Moderate

A

$\frac{105}{176} R^{5} ρ$
B

$\frac{105}{176} R^{2} ρ$
C

$\frac{176}{105} R^{5} ρ$
D

$\frac{186}{105} R^{2} ρ$

Solution

$I = \frac{2}{5} M R^{2} = \frac{2}{5} (\frac{4}{3} π R^{3} ρ) R^{2} = \frac{8}{15} π R^{5} ρ$
$I = \frac{176}{105} R^{5} ρ$ $(∵ π = \frac{22}{7})$

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