Three equal masses m are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At t=0, they are given an initial velocity V A=V0 A C, V B=V0 B A and V C=V0 C B. Here, A C, C B and B A are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is:

(A) 3 \mathrm{a} \mathrm{m} \mathrm{V}_0

(B) \frac{3}{2} a \mathrm{m} \mathrm{V}_0

(D) \frac{1}{2} a \mathrm{mV}_0

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JEE Mains · Physics · STD 11 - System of particles and rotational motion

JEE Mains 2025
Hard
MCQ

Three equal masses \(m\) are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At \(t=0\), they are given an initial velocity \(\vec{V}_A=V_0 \overrightarrow{A C}, \vec{V}_B=V_0 \overrightarrow{B A}\) and \(\vec{V}_C=V_0 \overrightarrow{C B}\). Here, \(\overrightarrow{A C}, \overrightarrow{C B}\) and \(\overrightarrow{B A}\) are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is :

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Correct Answer

(C) \(\frac{\sqrt{3}}{2}\) a \(\mathrm{m} \mathrm{V}_0\)

Step-by-step Solution

Detailed explanation

\(d=\frac{a}{2 \sqrt{3}}\)
Angular momentum of one mass about point \(O\)
\(\begin{aligned}
L & =m v d \\
& =m v_0 \cdot \frac{a}{2 \sqrt{3}}
\end{aligned}\)

Net angular momentum about point \(O\)
\(\begin{aligned}
L_{\text {net }} & =32 \\
& =\frac{\sqrt{3} m v_0 a}{2}
\end{aligned}\)

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