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

Rotational symmetry refers to how an object looks after it is rotated by a certain angle about a fixed point or axis. In the case of 4-fold rotational symmetry, the object must appear identical after a 90-degree rotation. Let's analyze the options:
Option (A) does not exhibit 4-fold symmetry, as rotating it by 90 degrees results in a different orientation.
Option (B) exhibits 4-fold symmetry. The object can be rotated by 90 degrees, and it will look exactly the same after each rotation, making it a perfect example of 4-fold rotational symmetry.
Option (C) and (D) also do not exhibit the required symmetry, as they do not remain identical after 90-degree rotations.
Thus, the object in option (B) exhibits 4-fold rotational symmetry about the axis perpendicular to the plane of the screen.
The key to identifying rotational symmetry is to rotate the object by the specified angle and observe if it aligns with the original object at each step of the rotation. If it does, the object has the corresponding rotational symmetry.