Four identical solid spheres each of mass m and radius a are placed...

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 : Four identical solid spheres each of mass m and radius a are placed with their centres on the four corners of a square

Four identical solid spheres each of mass m and radius a are placed with their centres on the four corners of a square

Options

A $\dfrac{8}{5}m{a}^{2} + m{b}^{2}$
B $\dfrac{4}{5}m{a}^{2} + 2m{b}^{2}$
C $\dfrac{8}{5}m{a}^{2} + 2m{b}^{2}$
D $\dfrac{4}{5}m{a}^{2}$

Correct answer

C. $\dfrac{8}{5}m{a}^{2} + 2m{b}^{2}$

Step-by-step solution

Four identical solid spheres each of mass m and radius a are placed with their centres on the four corners of a square

$I = 2 \times \left(\dfrac{2}{5}m{a}^{2}\right) + 2 \times \left(\dfrac{2}{5}m{a}^{2} + m{b}^{2}\right)$

$I = \dfrac{8}{5}m{a}^{2} + 2m{b}^{2}$

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