3 particles each of mass m are kept at ver

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$3$ particles each of mass $m$ are kept at vertices of an equilateral triangle of side $L$. The gravitational field at centre due to these particles is

A

Zero

B

$\frac{{3GM}}{{{L^2}}}$

C

$\frac{{9GM}}{{{L^2}}}$

D

$\frac{{12}}{{\sqrt 3 }}\,\frac{{GM}}{{{L^2}}}$

$3$ particles each of mass $m$ are kept at vertices of an equilateral triangle of side $L$. The gravitational field at centre due to these particles is

Due to three particles net intensity at the centre
$I = {\vec I_A} + {\vec I_B} + {\vec I_C} = 0$
because out of these three intensities one equal in magnitude and the angle between each other is $120^\circ$.