Question

Which of the following quantities measured from different inertial reference frames are the same?

• A. Force
• B. Velocity
• C. Displacement
• D. Kinetic energy

Answer 1

Answer: (A), (D)

Kinetic energy

Explanation for the correct options:

In case of option A.

1. The force is a vector under rotations and nothing happens to it under Galilean boosts.
2. The reason is that adding a constant to the velocity doesn't change the rate of change of velocity, which is the acceleration.
3. Hence, option A is the correct option.

In case of option D.

1. The kinetic energy of any entity depends on the reference frame in which it is measured.
2. However, the total energy of an isolated system, i.e., one in which energy can neither enter nor leave, does not change over time in the reference frame in which it is measured.
3. Hence, option D is the correct option.

Explanation for the incorrect options:

In case of option B

1. The velocity of bodies as seen by the different observers does depend on the relative motion of the two reference frames.
2. This means that it can vary in different inertial frames.
3. Hence, option B is the incorrect option.

In case of option C

1. Displacement of bodies also as seen by the different observers, does depend on the relative motion of the two reference frames.
2. This means that it can vary in different inertial frames.
3. Hence, option B is the incorrect option.

Thus, options A and D are correct options.