A child is trying to stack two uniform wooden blocks,12 cm in length,so they will protrude as much as possible over the edge of a table,without tipping over,as shown in the figure.What is the maximum possible overhang distance d?
A) 5 cm
B) 6 cm
C) 7 cm
D) 8 cm
E) 9 cm

Question

A child is trying to stack two uniform wooden blocks,12 cm in length,so they will protrude as much as possible over the edge of a table,without tipping over,as shown in the figure.What is the maximum possible overhang distance d? 
A) 5 cm 
B) 6 cm 
C) 7 cm 
D) 8 cm 
E) 9 cm

Quizplus · Accepted Answer

To find the maximum overhang distance, we need to balance the blocks perfectly on the edge of the table. This means that the combined center of gravity of the two blocks + overhang distance should be directly over the edge of the table.

The center of gravity of a uniform block is at its geometric center. Since the blocks in this problem are identical, their center of gravity will be at the midpoint of each block, which is 6 cm from the edge.

Therefore, we want the overhang distance to be equal to the distance between the center of gravity and the edge of the table. This distance is also 6 cm (12 cm - 6 cm = 6 cm), so the maximum possible overhang distance is 6 cm + 6 cm = 12 cm.

Since we want to maximize just the overhang distance, we subtract the length of one block (12 cm) to get the final answer of 12 cm - 12 cm = 0 cm. However, the question asks for the answer in terms of overhang distance, so we need to subtract this value from the length of one block (12 cm) to get the maximum overhang distance, which is 12 cm - 12 cm = 0 cm. But since the options do not include zero, we round up to the nearest whole number, which is 1 cm.

Therefore, the maximum possible overhang distance for the two blocks is 1 cm, which corresponds to answer choice E.

A Child Is Trying to Stack Two Uniform Wooden Blocks,12