Question

Which of the following are necessary conditions for a particle performing periodic motion?

(i) The particle's path is fixed

(ii) The particle's momentum is constant

(iii) Velocity at any position is same after time t = T time duration where T is particle's Time period.

(iv) Time period is same for every cycle

• A. All of these
• B. (i), (ii), (iv)
• C. (i), (iv)
• D. (i), (iii), (iv)

Answer 1

The correct option is D

(i), (iii), (iv)

For a periodic motion, the motion of particle should repeat itself, meaning after every time period 'T' the particle should be in the same position and should have the same velocity vector

If the above is true the path of the particle has to be fixed. So condition I is correct. The particle may accelerate and decelerate as long as it comes

back to the same position with same velocity vector after a time period 'T'.

So condition II is wrong. Momentum can change from the above discussion. Condition III is correct. Periodic motion means that the motion repeats after a fixed time period T. So condition IV is correct.

(i), (iii), (iv)