Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :

Question

Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is : (A) (4/5) ma 2+2 mb 2 (B) (8/5) m a2+m b2 (C) (8/5) ma 2+2 mb 2 (D) (4/5) ma 2

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/81079b1ecfa2fe1f7be0dba503843177-.png" /> I =2 ×((2/5) ma 2)+2 ×((2/5) ma 2+ mb 2) I =(8/5) ma 2+2 mb 2

Q. Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :

$\frac{4}{5} m a^{2} + 2 m b^{2}$

$\frac{8}{5} m a^{2} + m b^{2}$

$\frac{8}{5} m a^{2} + 2 m b^{2}$

$\frac{4}{5} m a^{2}$

$I = 2 \times (\frac{2}{5} m a^{2}) + 2 \times (\frac{2}{5} m a^{2} + m b^{2})$
$I = \frac{8}{5} m a^{2} + 2 m b^{2}$

Q. Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :

54​ma2+2mb2

58​ma2+mb2

58​ma2+2mb2

54​ma2

I=2×(52​ma2)+2×(52​ma2+mb2) I=58​ma2+2mb2

$\frac{4}{5} m a^{2} + 2 m b^{2}$

$\frac{8}{5} m a^{2} + m b^{2}$

$\frac{8}{5} m a^{2} + 2 m b^{2}$

$\frac{4}{5} m a^{2}$

$I = 2 \times (\frac{2}{5} m a^{2}) + 2 \times (\frac{2}{5} m a^{2} + m b^{2})$
$I = \frac{8}{5} m a^{2} + 2 m b^{2}$