Question

Which of the following is/are necessary and sufficient condition(s) for pure translation?

• A. The relative position of particles of the body does not change with time.
• B. Velocities of all the particles are parallel to each other at any given instant.
• C. A body always remains parallel to itself throughout its motion.
• D. Velocities of all the points of the body at any instant of time are equal.

Answer 1

Answer: (A), (B), (C), (D)

Velocities of all the points of the body at any instant of time are equal.

Thethree most basic criteria are

a) All the particles of the body have same velocity $\overrightarrow{v}$ at any instant.

b) Body should be parallel to itself throughout the motion.

c) Velocities of all the particles at any instant are equal.

Also a rigid body (rigid in the given condition throughout its motion) will only satisfy the above mentioned criteria.