Q.At a given instant three point masses m, 2m and 3m are equidistant from each other. Consider only the gravitational forces between them. Select correct statement/s for this instance only: (A) Mass m experiences maximum force. (B) Mass 2m experiences maximum force. (C) Mass 3m experiences maximum force. (D) All masses experience force of same magnitude.

[!TLDR] Comparing the resultant of each mass's two pairwise gravitational pulls (via the law of cosines at the 60-degree angle of the equilateral arrangement), mass 3m -- pulled by the two LARGEST pairwise forces -- experiences the largest net force. [!ANSWER] (C) Mass 3m experiences maximum force.

By Newton's law of gravitation, the pairwise force between any two masses depends on the PRODUCT of the two masses. With masses m, 2m, 3m mutually equidistant (say, separation d), the three pairwise force magnitudes are: between m & 2m: $F_{12}=\frac{G(m)(2m)}{d^2}=\frac{2Gm^2}{d^2}$; between m & 3m: $F_{13}=\frac{G(m)(3m)}{d^2}=\frac{3Gm^2}{d^2}$; between 2m & 3m: $F_{23}=\frac{G(2m)(3m)}{d^2}=\frac{6Gm^2}{d^2}$. The NET force on mass m is the vector sum of $F_{12}$ and $F_{13}$ (magnitudes $2Gm^2/d^2$ and $3Gm^2/d^2$, at 60 degrees to each other, the internal angle of the equilateral triangle formed by the three mutually-equidistant masses); the net force on 2m is the vector sum of $F_{12}=2Gm^2/d^2$ and $F_{23}=6Gm^2/d^2$; the net force on 3m is the vector sum of $F_{13}=3Gm^2/d^2$ and $F_{23}=6Gm^2/d^2$. Using the law of cosines, $|\vec{F}_{net}|=\sqrt{F_a^2+F_b^2+2F_aF_b\cos60^\circ}$ (attractive forces point toward each other, so the included angle between the two force vectors on a given mass equals the triangle's own 60-degree angle), gives (in units of $Gm^2/d^2$): on mass m, $\sqrt{2^2+3^2+2(2)(3)(0.5)}=\sqrt{19}\approx4.36$; on mass 2m, $\sqrt{2^2+6^2+2(2)(6)(0.5)}=\sqrt{52}\approx7.21$; on mass 3m, $\sqrt{3^2+6^2+2(3)(6)(0.5)}=\sqrt{63}\approx7.94$. The largest resultant is on mass 3m, since it is pulled by the two LARGEST individual pairwise forces ($3Gm^2/d^2$ and $6Gm^2/d^2$). [!ANSWER] (C) Mass 3m experiences maximum force.

Compute the three pairwise gravitational forces from $F=Gm_1m_2/d^2$, then vector-add (law of cosines, 60 degree included angle for an equilateral arrangement) the two forces acting on each mass to compare resultants.

Confusing 'force experienced' with 'acceleration produced' (dividing by the body's own mass) -- the question asks about force, not acceleration, so the heaviest mass, pulled by the two strongest pairwise attractions, experiences the largest net force even though its resulting acceleration would be comparatively smaller.