Four particles, each of mass $m,$ are kept at the four corners of a square of edge $a .$ Moment of inertia of the system about the line perpendicular to the plane of the square and passing through the centre of the square is.

3 m a^{2}

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2 m a^{2}

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4 m a^{2}

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8 m a^{2}

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Solution

The correct option is B $2 m a^{2}$
The perpendicular distance of every particle from the given line is $\frac{a}{\sqrt{2}}$

The moment of inertia of one particle is $m (\frac{a}{\sqrt{2}})^{2}$ = $\frac{m a^{2}}{2}$

The moment of intertia of system is therefore = $2 m a^{2}$

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Four particles, each of mass m, are kept at the four corners of a square of edge a. Moment of inertia of the system about the line perpendicular to the plane of the square and passing through the centre of the square is.

The correct option is B 2ma2The perpendicular distance of every particle from the given line is a√2 The moment of inertia of one particle is m(a√2)2 = ma22 The moment of intertia of system is therefore = 2ma2

Four particles, each of mass $m,$ are kept at the four corners of a square of edge $a .$ Moment of inertia of the system about the line perpendicular to the plane of the square and passing through the centre of the square is.

The correct option is B $2 m a^{2}$
The perpendicular distance of every particle from the given line is $\frac{a}{\sqrt{2}}$

The moment of inertia of one particle is $m (\frac{a}{\sqrt{2}})^{2}$ = $\frac{m a^{2}}{2}$

The moment of intertia of system is therefore = $2 m a^{2}$