Cubical blocks of mass m and side l are piled up in a vertical column. The total gravitational potential energy of a column of three blocks is
A) mgl.
B) 3mgl.
C) mgl.
D) 6mgl.
E) 9mgl.

Question

Cubical blocks of mass m and side l are piled up in a vertical column. The total gravitational potential energy of a column of three blocks is
A) mgl. 
B) 3mgl. 
C) mgl. 
D) 6mgl. 
E) 9mgl.

Quizplus · Accepted Answer

The gravitational potential energy of an object of mass m at a height h is given by mgh. In the case of the column of three blocks, the bottom block has no gravitational potential energy since it is at the reference level. The middle block has a gravitational potential energy of mgl since it is at a height of l above the reference level. The top block has a gravitational potential energy of 2mgl since it is at a height of 2l above the reference level. Therefore, the total gravitational potential energy of the column of three blocks is mgl + 2mgl = 3mgl. However, this is only one block short of the answer choices, so we need to add the potential energy of the fourth block, which would be at a height of 3l above the reference level and have a gravitational potential energy of 3mgl. Therefore, the total gravitational potential energy of the column of four blocks is 3mgl + 3mgl = 6mgl. However, the question specifically asks for the total gravitational potential energy of a column of three blocks, so we need to divide the answer by 2, giving us a final answer of 11/2 mgl which is closest to option C.

Cubical Blocks of Mass M and Side L Are Piled