Question

The magnitude and direction of acceleration change in the case of an object

• A. executing simple harmonic motion
• B. in circular motion at constant speed
• C. falling under gravity from lower altitudes
• D. falling under gravity from higher altitudes
• E. falling in a viscous liquid medium

Hint:

In SHM, acceleration is maximum at the extreme positions and zero at the mean position.
Its direction always points opposite to the displacement.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Acceleration is a vector quantity, meaning it has both magnitude and direction.
If either changes, the acceleration vector is considered to be changing.

Step 3: Detailed Explanation:
1. Simple Harmonic Motion (SHM): In SHM, the acceleration is given by \( a = -\omega^2 x \).
The magnitude depends on the displacement \( x \), so it changes as the object moves.
The direction is always towards the mean position, so it reverses whenever the object passes the mean position.
Thus, both magnitude and direction change.
2. Uniform Circular Motion: The magnitude of centripetal acceleration is constant (\( v^2/R \)), but its direction changes continuously (always towards the center).
3. Falling under gravity (low altitude): Both magnitude (\( g \approx 9.8 \text{ m/s}^2 \)) and direction (downwards) are roughly constant.
4. Viscous liquid: As the object reaches terminal velocity, acceleration eventually becomes zero.

Step 4: Final Answer:
An object executing simple harmonic motion experiences changes in both the magnitude and direction of its acceleration.