Periodic time of body moving with simple harmonic motion, is A. Directly proportional to its angular velocity B. Directly proportional to the square of its angular velocity C. Inversely proportional to the square of its angular velocity D. Inversely proportional to its angular velocity

The correct answer is: D. Inversely proportional to its angular velocity.

The period of a simple harmonic motion is the time it takes for an object to complete one full cycle of its motion. It is denoted by $T$. The angular velocity of a simple harmonic motion is the rate at which the object’s angle changes with time. It is denoted by $\omega$.

The relationship between the period and the angular velocity is given by the following equation:

$$T = \frac{2\pi}{\omega}$$

This equation shows that the period is inversely proportional to the angular velocity. This means that as the angular velocity increases, the period decreases.

Here is a diagram that shows the relationship between the period and the angular velocity:

[Diagram of a sine wave with the period and angular velocity labeled]

The period is the time it takes for the object to go from one peak to the next, or from one trough to the next. The angular velocity is the rate at which the object’s angle changes with time. The higher the angular velocity, the faster the object moves.

I hope this explanation is helpful! Let me know if you have any other questions.