Four particles A, B, C, D of mass $\frac{m}{2}$, $m$, $2m$, $4m$ have the same momentum, respectively. The particle with maximum kinetic energy is:
- D
- C
- A
- B
The Correct Option is C
Solution and Explanation
The kinetic energy is given by:
\[ KE = \frac{p^2}{2m} \]
Since all particles have the same momentum, the kinetic energy is inversely proportional to their mass:
\[ KE \propto \frac{1}{m} \]
Thus, the particle with the smallest mass will have the maximum kinetic energy.
Among the given particles:
\[ m_A = \frac{m}{2}, \quad m_B = m, \quad m_C = 2m, \quad m_D = 4m \]
Hence, \(\frac{m}{2}\) (particle A) has the maximum kinetic energy.
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