Question

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. $12\sqrt{2}$
• B. 12
• C. $10\sqrt{2}$
• D. $24\sqrt{2}$

Hint:

Resultant of two perpendicular vectors $P$ is $P\sqrt{2}$.

Answer 1

The Correct Option is A

Masses are 4kg, 4kg, 6kg.
Momentum vectors of equal masses: $\vec{p}_1 = 72\hat{i}$, $\vec{p}_2 = 72\hat{j}$.
Conservation: $\vec{p}_1 + \vec{p}_2 + \vec{p}_3 = 0$.
$\vec{p}_3 = -(72\hat{i} + 72\hat{j})$.
$|\vec{p}_3| = 72\sqrt{2}$.
$v_3 = \frac{72\sqrt{2}}{6} = 12\sqrt{2}$ m/s.