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

Question

Four point masses, each of value m, are placed at the comers of square ABCD of side l. The moment of inertia of this system about an axis passing through A and parallel to BD is (A) 2 ml2  (B)  √3 ml2  (C) 3 ml2 (D)  ml2

Tardigrade Admin · Accepted Answer

The situation is shown in figure. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/9660581ca121c4cfd8704efa181f7982-.png" /> Ix x prime =m × D P2+m × B Q2+m × C A2 =m × 2 ×((√2 l/2))2+m ×(√2 l)2 =3 m l2

Q. Four point masses, each of value $m$ , are placed at the comers of square $A BC D$ of side $l$ . The moment of inertia of this system about an axis passing through $A$ and parallel to $B D$ is

$2 m l^{2}$

$3 m l^{2}$

$3 m l^{2}$

$m l^{2}$

The situation is shown in figure.

$I_{x x^{'}} = m \times D P^{2} + m \times B Q^{2} + m \times C A^{2}$
$= m \times 2 \times (\frac{2 l}{2})^{2} + m \times (2 l)^{2}$
$= 3 m l^{2}$

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

2ml2

3​ml2

3ml2

ml2

The situation is shown in figure. Ixx′​=m×DP2+m×BQ2+m×CA2 =m×2×(22​l​)2+m×(2​l)2 =3ml2

Q. Four point masses, each of value $m$ , are placed at the comers of square $A BC D$ of side $l$ . The moment of inertia of this system about an axis passing through $A$ and parallel to $B D$ is

$2 m l^{2}$

$3 m l^{2}$

$3 m l^{2}$

$m l^{2}$

The situation is shown in figure.

$I_{x x^{'}} = m \times D P^{2} + m \times B Q^{2} + m \times C A^{2}$
$= m \times 2 \times (\frac{2 l}{2})^{2} + m \times (2 l)^{2}$
$= 3 m l^{2}$