IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

# Balancing the Nails

## Objective

To study concept of centre of mass.

## Apparatus

14 Nails and a stand.

## Procedure

Can you balance 14 nails on a nailhead? Fix a nail on a piece of wood or some lid so that it remains vertical with its flat top up. We will call this arrangement stand. Now, ask your friends to balance the remaining 14 nails on the nail fixed to the stand. Your friends will be a real fix attempting to put so many nails in a very small space. But, you come to their rescue by demonstrating how this can be done.

1. Fix a nail on a piece of wood or some lid so that it remains vertical with its flat top up. We will call this arrangement stand.
2. Now, ask your friends to balance the remaining nails on the nail fixed to the stand. Your friends will be a real fix attempting to put so many nails in a very small space. But, you come to their rescue by demonstrating how this can be done.
3. Place a nail on a table so that its head it towards you. We may call it base nail.
4. Now, arrange the remaining 12 nail, over the base nail on the left and right of it in such a manner that the heads of all the nails are towards the base nail. Place the head of the right nail on the base nail then the head of the left nail on the base nail, again the head of the right nail, then the head of the left nail, and so on, till you have placed all the 12 nails on the base nail.
5. Now, place the fourteenth nail on the base nail in such a manner that its sharp end is towards the head of the base nail. In this way all the twelve nail will come between the base nail and the upper nail.
6. Pressing both the base nail and the upper nail against each other and holding them with both you hand carefully place the entire set of nails at the mid print of the base nail fixed to the stand. Withdraw both your hands slowly. The pointed or sharp ends of the nails get lowered on both the left and right sides and their blunt and flat ends get entangled with one another. The entire set of nail resting on the base nail balances on the nail stuck to the stand. Surprising, isn't it?

In this experiment the principle of centre of gravity plays its role. According to this principle, due to the weight of the inclined nails on both sides of the base nail the weight of the entire set-up acts below the balancing point. Thus, the entire set of nails balances comfortably. You may gently lower the nails on one side and then remove your hand. This makes the entire set-up quiver but it does not fall down.

## Concepts

Centre of Mass, Torque, Stable Equilibrium

## Note

Puzzle: Ask students to pin-point centre of mass of the structure when Nail are horizontal/slanted. Generally, students points at geometrical centre in first case. In second case, they do not give a thought about third direction. The CM is out of the structure. Also, we can explain about concept of stable/unstable equilibrium, torqe, potential energy etc.