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

# Counter-intutive Centre of Mass with Bottles

## Objective

Centre of mass and stability.

## Apparatus

PVC pipe of 30 cm length and 4 cm diameter, two half litre water bottles.

## Procedure

Take a PVC pipe and make two holes to fit bottle caps. Cut one end of the PVC pipe at 45 degree. Take half litre bottle full of water and put it in the lower hole. The bend pipe balances it. Take another bottle and place it in the upper hole. Both the bottles balances the bend pipe.

## Discussion

The balancing conditions are (a) net force on the body should be zero and (b) net torque on the body should be zero. Let us consider pipe and the bottles as a system. The forces acting on the system are normal reaction $$N$$ at the base (in vertically upward direction) and weight $$mg$$ acting at the centre of mass (vertically downward). Net force is zero if $$N=mg$$. The torque due to $$mg$$ and $$N$$ balances each other only if they are in the same vertical line. The point of action of the normal reaction is confined to the pipe area in contact with the ground (it cannot act outside it). Thus, centre of mass should lie vertically above the contact area for net torque to become zero.