Which of the following correctly defines relativistic kinetic energy?

The correct option is based on understanding the concept of relativistic kinetic energy, which pertains to the kinetic energy of an object moving at a significant fraction of the speed of light. In relativistic physics, the kinetic energy of an object is given by the equation:

[ KE = \gamma m_0 c^2 - m_0 c^2 ]

where ( \gamma ) (the Lorentz factor) is defined as ( \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} ), ( m_0 ) is the rest mass of the object, and ( c ) is the speed of light.

The expression in option B simplifies to show that the relativistic kinetic energy increases as an object's speed approaches the speed of light. This contrasts sharply with classical kinetic energy, where an object at rest has zero kinetic energy. As speed increases, the relativistic effects become significant, and the simple quadratic relationship from classical physics (as seen in ( \frac{1}{2} mv^2 )) is no longer adequate to describe the energy.

In summary, option B accurately reflects the change in energy as an object accelerates toward significant velocities, showcasing the principles of relativ