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

Answer: (C)

A

Answer 2

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.