Question

An alphabet 'a' made of two similar thin uniform metal plates of each length \( L \) and width \( a \) is placed on a horizontal surface as shown in the figure. If the alphabet is vertically inverted, the shift in the position of its center of mass from the horizontal surface is:

• A. \( \frac{L - a}{2} \)
• B. \( \frac{a - L}{2} \)
• C. \( \frac{L - a}{2} \)
• D. \( L - a \) \bigskip

Hint:

The shift in the position of the center of mass of the inverted 'a' is calculated by finding the difference between the center of mass of the horizontal plate and the vertical plate

Answer 1

The Correct Option is A

The center of mass of the 'a' is the combined center of mass of two parts:
1. The horizontal plate with length \( L \) and width \( a \).
2. The vertical plate with length \( L \) and width \( a \). The total mass of each plate is proportional to its area. Let the masses of the horizontal and vertical plates be \( m_1 \) and \( m_2 \), respectively. When the alphabet ‘T’ is placed on the horizontal surface, the center of mass is at a certain position. Upon inverting the alphabet, the center of mass shifts accordingly. The shift in the position of the center of mass of the inverted â is calculated by finding the difference between the center of mass of the horizontal plate and the vertical plate. Since the plates are uniform, the center of mass of the horizontal plate is at \( \frac{L}{2} \) from one edge, and for the vertical plate, the center of mass is at \( \frac{L + a}{2} \). After calculating, we find that the shift in the position of the center of mass from the horizontal surface is \( \frac{L - a}{2} \).