JEE Main 2026 — Jan 23, Shift 2 — Physics solution

JEE Main2026Jan 23, Shift 2Physics

A body of mass $14$ kg initially at rest explodes and breaks into three fragments of masses in the ratio $2 : 2 : 3$ . The two pieces of equal masses fly off perpendicular to each other with a speed of $18$ m/s each. The velocity of the heavier fragment is ____ m/s.

A
$102$
B
$122$
C
$12$
D
$242$

Solution

Masses are $4, 4, 6$ kg (totalling 14 kg). Let the two equal pieces move along $- \hat{i}$ and $- \hat{j}$ with speed $18$ m/s. Momentum conservation from rest:

$4 (- 18 \hat{i}) + 4 (- 18 \hat{j}) + 6 V_{3} = 0$

$V_{3} = \frac{72 i ^ + 72 j ^}{6} = 12 \hat{i} + 12 \hat{j}$ .

$∣ V_{3} ∣ = 1 2^{2} + 1 2^{2} = 122$ m/s.

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