Four particles,each of mass 1 kg,are placed | vedclass

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(B) Let the mass of each particle be $m = 1 \ kg$ and the side of the square be $a = 2 \ m$.Let the axis of rotation pass through one of the vertices

Vedclass · Accepted Answer

$16$

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(B) Let the mass of each particle be $m = 1 \ kg$ and the side of the square be $a = 2 \ m$.Let the axis of rotation pass through one of the vertices (say,the top-right corner) and be perpendicular to the plane of the square.The distances of the four particles from this axis are:$1$. The particle at the axis: $r_1 = 0$$2$. The two adjacent particles: $r_2 = r_3 = a = 2 \ m$$3$. The diagonally opposite particle: $r_4 = \sqrt{a^2 + a^2} = a\sqrt{2} = 2\sqrt{2} \ m$The moment of inertia $I$ is given by $I = \sum m_i r_i^2 = m(r_1^2 + r_2^2 + r_3^2 + r_4^2)$.$I = 1 	imes (0^2 + 2^2 + 2^2 + (2\sqrt{2})^2)$$I = 1 	imes (0 + 4 + 4 + 8) = 16 \ kg \ m^2$.

Four particles,each of mass $1 \ kg$,are placed at the four corners of a square of side $2 \ m$. The moment of inertia of the system about an axis perpendicular to its plane and passing through one of its vertices is . . . . . . $kg \ m^2$.

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