When the balance is at rest, the reading on the scale is equal to the weight of the object being weighed. This weight is equal to the force of gravity acting on the object, which is given by the equation:
$$W = mg$$
where:
- $W$ is the weight of the object in newtons (N)
- $m$ is the mass of the object in kilograms (kg)
- $g$ is the acceleration due to gravity in meters per second squared (m/s²)
If the balance is accelerating downwards at a rate of $g$, the force of gravity acting on the object will be counteracted by the force of inertia acting on the object. This force of inertia is given by the equation:
$$F = ma$$
where:
- $F$ is the force of inertia in newtons (N)
- $m$ is the mass of the object in kilograms (kg)
- $a$ is the acceleration of the object in meters per second squared (m/s²)
Since the force of gravity and the force of inertia are equal in magnitude and opposite in direction, the net force acting on the object will be zero. This means that the object will remain at rest relative to the balance, and the reading on the scale will be zero.
