Question

A steel solid sphere of diameter \(2\) cm collides head-on elastically with another steel solid sphere of radius \(2\) cm at rest. The fraction of the initial kinetic energy of the smaller sphere transferred to the larger sphere during collision is

• A. \(\dfrac{16}{27}\)
• B. \(\dfrac{16}{9}\)
• C. \(\dfrac{8}{9}\)
• D. \(\dfrac{32}{81}\)

Hint:

For a one-dimensional elastic collision where the second body is initially at rest, \[ \boxed{ \text{Fraction of kinetic energy transferred} = \frac{4m_1m_2}{(m_1+m_2)^2}. } \] For solid spheres of the same material, \[ \boxed{m\propto r^3.} \]

Answer 1

The Correct Option is D