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 AC , overrightarrow CB and overrightarrow BA 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 :

Physics · Rotational Dynamics

JEE Main 2025 — 29 January, Evening Shift — Question 31

Three equal masses $m$ are kept at vertices (A, B, C) of an equilateral triangle of side $a$ in free space. At $\mathrm{t}=0$ , they are given an initial velocity $\vec{V}_{A}=V_{0} \overrightarrow{A C}, \quad \vec{V}_{B}=V_{0} \overrightarrow{B A}$ and $\vec{V}_{C}=V_{0} \overrightarrow{C B}$ . Here, $\overrightarrow{\mathrm{AC}}, \overrightarrow{\mathrm{CB}}$ and $\overrightarrow{\mathrm{BA}}$ 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 :

Option A:
$\frac{1}{2} \mathrm{amV}_{0}$
Option B:
3 a m V
Option C:
$\frac{\sqrt{3}}{2} a \mathrm{mV}_{0}$
Correct
Option D:
$\frac{3}{2} \mathrm{amV}_{0}$

Answer: C

Step-by-step solution

$\tan 30^{\circ}=\frac{2 \mathrm{r}}{\mathrm{a}}=\frac{1}{\sqrt{3}}$

$r=\frac{a}{2 \sqrt{3}}$

$\mathrm{L}=\left(\operatorname{mvr}_{\perp}\right) \times 3$

$=m v_{0} \frac{a}{2 \sqrt{3}} \times 3$

$=\frac{\sqrt{3}}{2} \mathrm{mv}_{0} \mathrm{a}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 29 January, Evening Shift
Subject: Physics
Chapter: Rotational Dynamics
Topic: Angular Momentum and its Conservation