Question
Uniform and identical sticks each of length 25cm are stacked, so that 8cm of each stick extends beyond the stick beneath as shown in Figure.
How many maximum numbers of sticks can be placed one over the other without making them to fall over?
Solution
The given meter sticks are identical to each other.
The centre of gravity of each stick is located at its mid point.
The system is as shown in the figure below.
The centre of gravity of each stick is located at its mid point.
The system is as shown in the figure below.
Let 'n' be the maximum numbers of sticks that can be placed one over the other without making them topple.
Let edge O of the lowest stick S1, on the floor, is the reference point.
The distances of centre of gravity of sticks S2, S3, S4......Sn are x2 = -4.5cm, x3 =3.5cm, x4= 11.5cm, ..., xn= -4.5+(8n.2) = (8n -20.5)cm respectively.
Let m be the mass of each stick.
The position of CG of sticks S2 S3, S4......Sn from the O is,
The position of CG of sticks S2, S3, S4......Sn should lie on left from edge of the S1 is the condition for the sticks to not topple.
i.e., X ≤ 0
4n -12 . 5 ≤ 0
n ≤ 3.125
n = 3
Hence on a maximum, three sticks can be stacked one over other.
