Physics

To determine in which scenarios the object's kinetic energy remains unchanged, we will analyze the kinetic energy formula:

where:

is the mass,

is the velocity.

We need to find out when the new kinetic energy equals the initial kinetic energy.

Let's analyze each scenario.

Option A: The mass remains unchanged, and the velocity increases to twice its original value.

- Initial kinetic energy:

- New kinetic energy with velocity doubled:

- Kinetic energy increases by a factor of 4.

Option B: The velocity remains unchanged, and the mass increases to twice its original value.

- Initial kinetic energy:

- New kinetic energy with mass doubled: