A stationary body of mass m explodes into 3 parts with mass...

A stationary body of mass $m$ explodes into 3 parts with mass ratio of $1: 3: 3$. The two fragments with equal mass move at right angles to each other with velocity of $15 \mathrm{~m} \mathrm{~s}^{-1}$. The velocity of the third fragment is $\left(\mathrm{m} \mathrm{s}^{-1}\right)$ (a) $\sqrt{2}$ (b) 5 (c) $20 \sqrt{2}$ (d) $45 \sqrt{2}$

A stationary body of mass $m$ explodes into 3 parts with mass ratio of $1: 3: 3$. The two fragments with equal mass move at right angles to each other with velocity of $15 \mathrm{~m} \mathrm{~s}^{-1}$. The velocity of the third fragment is $\left(\mathrm{m} \mathrm{s}^{-1}\right)$
(a) $\sqrt{2}$
(b) 5
(c) $20 \sqrt{2}$
(d) $45 \sqrt{2}$

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Key Concepts

Conservation of Momentum

This principle states that in an isolated system—with no external forces acting—the total momentum remains constant throughout any process, including explosions. Since the object is initially at rest, the vector sum of the momenta of the resulting fragments must equal zero after the explosion.

Vector Addition of Momentum

Momentum is a vector quantity, which means both its magnitude and direction are significant. In problems where fragments move in different directions, it is essential to break down and add their momentum components along mutually perpendicular axes, ensuring that the total momentum in each direction sums to zero.

Mass Ratios and System Decomposition

Understanding the relative mass distribution of the fragments is crucial in determining individual masses from a given ratio. This concept allows us to express fragment masses in terms of a common variable, which can then be used to relate their momenta to each other when applying conservation laws.

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