Question

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:

• A. D
• B. C
• C. A
• D. B

Answer 1

The Correct Option is C

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.