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

# Win a 100 Rs Note

## Introduction

For rotational equilibrium, the net torque acting on the body should be zero. For bodies kept on a plane surface, this condition is achieved when the vertical line through the centre of mass passes through the area of contact.

## Procedure

Stand with your heels touching a wall and feet together. Place a 100 Rs note on the floor about a foot in front of your feet. Now, try to pick up the 100 Rs note without moving your feet or bending your knees. You can't pick it up. This demo explains concept like centre of mass, static equilibrium, torque etc.

When you stand straight against the wall, your center of mass is over your feet (base) as it should be. When you bend forward, you move your center of mass forward. In order to keep your balance, you must move your feet forward too. This maintains the base under the center of mass needed for stability. If you persist in trying to pick it up, you'll fall flat on your face!

## Discussion

When a body is in equilibrium, the net force as well as net torque on it should be zero. When one stand on the floor, the forces acting are (i) Force due to gravity, $$mg$$ downward and (ii) force on the feet, $$N$$ upward. To make the torque zero, $$mg$$ must be in the same vertical line as $$N$$. When you bend forward having your feet at the same place on the floor, your centre of mass moves slightly forward. To make the torque zero, the point of action of $$N$$ also moves forward. But the point of action of $$N$$ cannot move beyond the foot (contact area of feet with ground). Thus, if you bend more, centre of mass goes beyond the foot and $$N$$ and $$mg$$ no longer remains in same vertical line. This produces non-zero torque which tends to make you fall forward. As your reflex system will not allow to do such thing which can cause injury, you stop bending.

What is the role of wall in this demonstration? When you are asked to stand with your back and legs touching the wall, you do not have the freedom to take your stomach or hips backward. In other words,you can't redistribute your mass to keep the centre of mass on line of action of normal force.