JEE Main 2025 Jan 29 Shift 2, Physics Q15: Angular Momentum, Its Conservation and Angular Impulse

JEE Main2025Jan 29, Shift 2Physics

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 $V_{A} = V_{0} A C$ , $V_{B} = V_{0} B A$ and $V_{C} = V_{0} C B$ . 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
$\frac{1}{2} am V_{0}$
B
$3 am V_{0}$
C
$\frac{3}{2} am V_{0}$
D
$\frac{3}{2} am V_{0}$

Solution

The three initial velocities are cyclically tangent to the centroid, so the configuration has three-fold rotational symmetry and the angular momentum about the centroid is conserved.

Each velocity vector points along an edge of the triangle. The perpendicular distance from the centroid to any side of an equilateral triangle of side $a$ is $\frac{a}{2 3}$ .

For each particle, contribution to angular momentum about the centroid:

$L_{i} = m V_{0} \cdot \frac{a}{2 3}$ .

By symmetry the three contributions all point in the same sense (out of the plane), so

$L_{net} = 3 m V_{0} \cdot \frac{a}{2 3} = \frac{3}{2} m V_{0} a$ .

Angular momentum is conserved throughout the motion, so this is also the magnitude at the moment of collision.

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JEE Main 2025 Jan 29 Shift 2, Physics Q15: Angular Momentum, Its Conservation and Angular Impulse

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