Answer:
The distance of the father from the center is [tex]d_f = \frac{1}{2} \ m[/tex]
Explanation:
From the question we are told that
The distance of the son from the center is [tex]d_s = 2 \ m[/tex]
Let the mass of the son be [tex]m_s[/tex]
then the mass of the father is [tex]m_f = 4m_s[/tex]
Now for the teeter-totter to be balanced the torque due to the weight of the father must be equal to the torque due to the weight the son, this is mathematically represented as
[tex]\tau_s = \tau_f[/tex]
Where [tex]\tau_s[/tex] is the torque of the son which is mathematically represented as
[tex]\tau_ s = m_s * d_s * g[/tex]
while [tex]\tau_f[/tex] is the torque of the father which is mathematically represented as
[tex]\tau_f = m_f * d_f * g[/tex]
=> [tex]\tau_f = 4 m_s * d_f * g[/tex]
So
[tex]4 m_s * d_f * g = m_s * d_s * g[/tex]
substituting values
[tex]4 * d_f * = 2[/tex]
=> [tex]d_f = \frac{1}{2} \ m[/tex]
