Question

A particle collides elastically with another particle at rest. If the masses of the particles be \( m_1 \) and \( m_2 \) respectively, then the fraction of kinetic energy transferred to the second will be maximum when:

• A. \( \frac{m_2}{m_1} = 1 \)
• B. \( \frac{m_2}{m_1} = 2 \)
• C. \( \frac{m_2}{m_1} = 0.5 \)
• D. \( \frac{m_2}{m_1} = 3 \)

Hint:

In elastic collisions, maximum energy transfer occurs when both colliding masses are equal.

Answer 1

The Correct Option is A

For elastic collisions, the fraction of kinetic energy transferred to the second mass is given by:
\[ K = \frac{4 m_1 m_2}{(m_1 + m_2)^2} \] To maximize \( K \), differentiate with respect to \( \frac{m_2}{m_1} \), and solving gives:
\[ m_1 = m_2 \] Thus, the kinetic energy transfer is maximum when \( m_1 = m_2 \), i.e.,