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Question
If the linear momentum of a particle is known, can you find its kinetic energy? If the kinetic energy of a particle is know can you find its linear momentum?
Solution
Yes, the kinetic energy of the particle can be determined if the value of linear momentum is known.
The kinetic energy is calculated using the formula:
\[K . E = \frac{1}{2}m v^2 = \frac{p^2}{2m}\]
\[\text{ where, p is the linear momemtum having value mv. }\]
But linear momentum cannot be determined even if the kinetic energy is known because linear momentum is a vector quantity, whereas kinetic energy is a scalar quantity. Thus, the direction of the linear momentum remains unknown, however its magnitude can be calculated.
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