A bomb of 12 kg divides in two parts whose ratio of masses...

A bomb of $12 \mathrm{~kg}$ divides in two parts whose ratio of masses is $1: 4 .$ If kinetic energy of smaller part is $288 \mathrm{~J}$, then momentum of bigger part in $\mathrm{kgm} / \mathrm{sec}$ will be
(A) 38
(B) 72
(C) 108
(D) Data is incomplete

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Key Concepts

Conservation of Momentum

In a closed system with no external forces, such as an explosion starting from rest, the total momentum must be conserved. This means that the vector sum of the momenta of all fragments after the explosion equals the initial momentum (which is zero), leading to equal and opposite momenta for pairs of fragments.

Kinetic Energy

Kinetic energy is the energy of an object due to its motion, expressed as KE = 1/2 mv². This concept allows one to determine the velocity of a moving object if its mass and kinetic energy are known, and vice versa.

Mass Ratio and Fragmentation

When a body breaks into parts with a given ratio of masses, the total mass is divided proportionally among the parts. This ratio is essential for determining the individual masses of the fragments, which in turn are used in calculations involving energy and momentum.

Relationship Between Kinetic Energy and Momentum

The momentum of an object (p = mv) is directly related to its velocity. By using the kinetic energy equation to determine the velocity, one can subsequently calculate the momentum. This connection is crucial when kinetic energy values are provided and momenta are sought.

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