A unifom pencil AB weighing 40g can be balanced horizontally on a knife adge at 2cm from the end A when a mass of 60g is hung from this end. What is the length of pencil?

Answer 1

Let the length of the pencil be x cm.

Since the pencil can be balanced horizontally on a knife edge at 2 cm from end A,
The moment about the knife edge due to the weight of the pencil (40g) is balanced by the moment about the knife edge due to the weight hanging from end A (60g).

The moment due to the weight of the pencil is given by: 40g * (x - 2) cm.
The moment due to the weight hanging from end A is given by: 60g * 2 cm.

Setting the two moments equal, we have:
40g * (x - 2) = 60g * 2.

Simplifying the equation:
40(x - 2) = 120,
40x - 80 = 120,
40x = 200,
x = 5.

Therefore, the length of the pencil is 5 cm.