Question 131: Centre of Mass and Rotational Motion

Question

Four equal masses, m each are placed at the comers of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be :

Accepted Answer

$$AC = \sqrt {{l^2} + {l^2}} $$
$$AC = l\sqrt 2 $$
$$d = {{l\sqrt 2 } \over 2}$$
$$ \Rightarrow d = {1 \over {\sqrt 2 }}$$
Moment of inertia about the axis passing through A :
$$I = m{(O)^2} + m{(d)^2} + m{(d)^2} + M{(AC)^2}$$
$$ \Rightarrow I = O + m{\left( {{l \over {\sqrt 2 }}} \right)^2} + m{\left( {{l \over {\sqrt 2 }}} \right)^2} + m{\left( {l\sqrt 2 } \right)^2}$$
$$ \Rightarrow I = {{m{l^2}} \over 2} + {{m{l^2}} \over 2} + 2m{l^2}$$
$$ \Rightarrow I = 3m{l^2}$$

Answer

$$\sqrt 3 $$ ml
2

Answer

2 ml
2

Answer

ml
2

Answer

3 ml
2

Centre of Mass and Rotational Motion

Four equal masses, m each are placed at the comers of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be :

Choose the correct answer: