To find the mass that would balance the lever, we can use the principle of moments. The moment (torque) is calculated as the product of the mass and the distance from the pivot.
Let's denote:
- \( m_1 = 10 \) kg (mass on one side)
- \( d_1 = 40 \) cm (distance from the pivot for \( m_1 \))
- \( m_2 \) (mass on the other side we need to find)
- \( d_2 = 60 \) cm (distance from the pivot for \( m_2 \))
According to the principle of moments, for the lever to be balanced: \[ m_1 \times d_1 = m_2 \times d_2 \]
Plugging in the values: \[ 10 , \text{kg} \times 40 , \text{cm} = m_2 \times 60 , \text{cm} \]
Calculating the left side: \[ 400 , \text{kg cm} = m_2 \times 60 , \text{cm} \]
Now, we can solve for \( m_2 \): \[ m_2 = \frac{400 , \text{kg cm}}{60 , \text{cm}} = \frac{400}{60} = \frac{20}{3} \approx 13.33 , \text{kg} \]
None of the provided options (20 kg, 5 kg, 15 kg, 10 kg) precisely equal 13.33 kg, but the closest option is 15 kg.
Therefore, the answer is: 15 kg.