Question 371: Centre of Mass and Rotational Motion

Question

Four point masses, each of value $$m,$$ are placed at the corners of a square $$ABCD$$ of side $$l$$. The moment of inertia of this system about an axis passing through $$A$$ and parallel to $$BD$$  is

Accepted Answer

Let $${I_{A}}$$ is the moment of inertia about an axis passing through A and parallel to BD.
$${I_{A}} = M.I\,$$ due to the point mass at $$B+$$
$$M.I$$ due to the point mass at $$D+$$
$$M.I$$ due to the point mass at $$C.$$
$${I_{A}} = 2 	imes m{\left( {{	extstyle{\ell  \over {\sqrt 2 }}}} ight)^2} + m{\left( {\sqrt 2 \ell } ight)^2}$$
$$ = m{\ell ^2} + 2m{\ell ^2} = 3m{\ell ^2}$$

Answer

$$2m{l^2}$$

Answer

$$\sqrt 3 m{l^2}$$

Answer

$$3m{l^2}$$

Answer

$$m{l^2}$$

Centre of Mass and Rotational Motion

Four point masses, each of value $m, are placed at the corners of a square ABCD of side l. The moment of inertia of this system about an axis passing through A and parallel to BD$ is

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