To solve this problem, we need to use the principle of moments (or moments of force) about the pivot point. The moments must balance each other for the balance to be level.
The formula for moment is: \[ \text{Moment} = \text{Force} \times \text{Distance from pivot} \]
In this case, the force is due to the weight of the mass (which is mass multiplied by the acceleration due to gravity, \( g \), but since \( g \) is the same for both sides, we can simplify and just use mass).
Let the mass at 60 cm be \( m \).
For the 4 kg mass at 30 cm: \[ \text{Moment}_{\text{left}} = 4 , \text{kg} \times 30 , \text{cm} = 120 , \text{kg·cm} \]
For the unknown mass \( m \) at 60 cm: \[ \text{Moment}_{\text{right}} = m \times 60 , \text{cm} \]
Setting the moments equal for balance: \[ 4 , \text{kg} \times 30 , \text{cm} = m \times 60 , \text{cm} \]
Now, substituting the values: \[ 120 , \text{kg·cm} = m \times 60 , \text{cm} \]
Solving for \( m \): \[ m = \frac{120 , \text{kg·cm}}{60 , \text{cm}} \] \[ m = 2 , \text{kg} \]
Therefore, the mass that would level the balance is 2 kg.