Question

An object is said to have an n-fold rotational symmetry if the object, rotated by an angle of \( \frac{2\pi}{n} \), is identical to the original. 
Which one of the following objects exhibits 4-fold rotational symmetry about an axis perpendicular to the plane of the screen? 
 

• A.
• B.
• C.
• D.

Hint:

When checking for rotational symmetry, try rotating the object by the required angle and see if the object matches its original position after each rotation.

Answer 1

The Correct Option is B

Understanding Rotational Symmetry: Rotational symmetry refers to an object's ability to look the same after being rotated by a certain angle about a fixed point or axis. 
4-Fold Rotational Symmetry: An object has 4-fold rotational symmetry if it looks identical after each 90-degree rotation. 
Analysis of Options:

• Option (A): Does not exhibit 4-fold symmetry, as a 90-degree rotation results in a different orientation.
• Option (B): Exhibits 4-fold symmetry. After each 90-degree rotation, the object looks identical, making it a perfect example.
• Option (C) & (D): Do not remain unchanged after 90-degree rotations, so they lack 4-fold symmetry.

Conclusion: The object in option (B) exhibits 4-fold rotational symmetry about the axis perpendicular to the plane of the screen. 
Key Insight: The key to identifying rotational symmetry is to rotate the object by the specified angle and check if it aligns with its original position at each step. If it does, it possesses that level of symmetry.