Question 28: Centre of Mass and Rotational Motion

Question

Three particles each of mass m are kept at the vertices of an equilateral triangle of side b. Moment of inertia of the system about an axis passing through the centroid and perpendicular to its plane is

Accepted Answer

Let us consider an equilateral $$\Delta$$ABC of side b.
From figure,
In $$\Delta$$AOD,
$$\cos 30^\circ  = {{AD} \over {AO}}$$
$$ \Rightarrow {{\sqrt 3 } \over 2} = {{{b \over 2}} \over r}$$ [$$\because$$ $$\cos 30^\circ  = {{\sqrt 3 } \over 2}$$]
$$ \Rightarrow r = {b \over 2} 	imes {2 \over {\sqrt 3 }} = {b \over {\sqrt 3 }}$$
Moment of inertia about line passing through centroid,
$$I = 3 	imes m{r^2}$$ [due to 3 masses present in system]
$$ \Rightarrow 3 	imes m 	imes {\left( {{b \over {\sqrt 3 }}} ight)^2}$$
$$ \Rightarrow I = m{b^2}$$

Answer

3 mb
2

Answer

mb
2

Answer

$${{m{b^2}} \over 3}$$

Answer

$${2 \over 3}$$ mb
2

Centre of Mass and Rotational Motion

Three particles each of mass m are kept at the vertices of an equilateral triangle of side b. Moment of inertia of the system about an axis passing through the centroid and perpendicular to its plane is

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