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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?
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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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