A body of mass 1 kg initially at rest explodes and breaks...

A body of mass $1 \mathrm{~kg}$ initially at rest explodes and breaks into three fregments of masses in the ratio $1: 1: 3$. The two pieces of equal mass fly off perpendicular to each other with a speed of $15 \mathrm{~ms}^{-1}$ each. The speed of the heavier fregment is (a) $45 \mathrm{~ms}^{-1}$ (b) $15 \mathrm{~ms}^{-1}$ (c) $5 \mathrm{~ms}^{-1}$ (d) $5 \sqrt{2} \mathrm{~ms}^{-1}$

A body of mass $1 \mathrm{~kg}$ initially at rest explodes and breaks into three fregments of masses in the ratio $1: 1: 3$. The two pieces of equal mass fly off perpendicular to each other with a speed of $15 \mathrm{~ms}^{-1}$ each. The speed of the heavier fregment is
(a) $45 \mathrm{~ms}^{-1}$
(b) $15 \mathrm{~ms}^{-1}$
(c) $5 \mathrm{~ms}^{-1}$
(d) $5 \sqrt{2} \mathrm{~ms}^{-1}$

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Key Concepts

Conservation of Momentum

In physics, the principle of conservation of momentum states that the total momentum of a closed system remains constant provided no external forces act on it. This concept is crucial when analyzing explosions or fragmentations, as the sum of the individual momenta of the resulting pieces must equal the momentum of the original body prior to the event.

Vector Decomposition

Momentum is a vector quantity, which means it has both magnitude and direction. When dealing with scenarios where fragments move in different directions, such as perpendicular directions, it is important to break down the momentum into its components along the coordinate axes. This makes it possible to apply conservation of momentum separately to each component, facilitating the calculation of unknown speeds or directions.

Mass Distribution

When a body breaks into fragments with different masses, the distribution of mass directly influences how momentum is shared among the fragments. Recognizing and using the given mass ratio helps determine the individual masses, which is essential for setting up the conservation equations and solving for the unknown quantities such as the velocity of one of the fragments.

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