Infinite numbers of bloks are placed on a table on a edge as shown in the diagram.

What is the minimum value of L so that the blocks are just going to topple over the table ?

Options

A. `x//3`
B. `2x//5`
C. `3x//7`
D. `4x//9`

Answer

C

Explanation

Centre of mass of combination should lie on edge of table.

`x_(COM) = 0`
`(x_(COM) = [m((x)/(2) -L) + (m)/(4) ((x)/(4) - L) + (m)/(16) ((x)/(8) -L)])/(sum M) = 0`
`(x)/(2)[1 + (1)/(8) + (1)/(8^(2)) + .......] - L [1 + (1)/(4) + (1)/(4^(2)) +......] = 0`
`(x)/(2) [(1)/(1 - (1)/(8))] - L [(1)/(1 - (1)/(4))] = 0`
`L = (3x)/(7)`