Three equal masses m are kept at vertices (A, | vedclass

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(C) The angular momentum of a particle about a point is given by $\vec{L} = \vec{r} 	imes \vec{p} = m(\vec{r} 	imes \vec{v})$.For each mass,the perp

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$\frac{\sqrt{3}}{2} a m V_0$

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(C) The angular momentum of a particle about a point is given by $\vec{L} = \vec{r} 	imes \vec{p} = m(\vec{r} 	imes \vec{v})$.For each mass,the perpendicular distance $r_{\perp}$ from the centroid of the equilateral triangle to the velocity vector (which lies along the side) is the distance from the centroid to the side.In an equilateral triangle of side $a$,the distance from the centroid to any side is $r_{\perp} = \frac{a}{2\sqrt{3}}$.The velocity of each mass is $V_0$ directed along the sides of the triangle.The angular momentum of one mass about the centroid is $L_1 = m V_0 r_{\perp} = m V_0 \left( \frac{a}{2\sqrt{3}} ight)$.Since the velocities are directed such that all three masses contribute to the angular momentum in the same rotational sense (clockwise or counter-clockwise),the total angular momentum is $L = 3 	imes L_1$.$L = 3 	imes m V_0 \left( \frac{a}{2\sqrt{3}} ight) = \frac{3}{2\sqrt{3}} m V_0 a = \frac{\sqrt{3}}{2} m V_0 a$.

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