Respuesta :
Answer:[tex]\frac{5L}{6}[/tex]
Explanation:
Given
Wooden board is pivoted at center and
Older child of mass [tex]M=32\ kg[/tex] is sitting at a distance of L from center
if two child of mass [tex]\frac{M}{2}[/tex] is sitting at a distance [tex]\frac{L}{6}[/tex] and [tex]x[/tex](say) from pivot then net torque about pivot is zero
i.e.
[tex]\Rightarrow \tau_{net}=MgL-\frac{M}{2}g\frac{L}{6}-\frac{M}{2}gx[/tex]
as [tex]\tau_{net}=0[/tex]
Therefore
[tex]MgL=\frac{M}{2}g\frac{L}{6}+\frac{M}{2}gx[/tex]
[tex]L-\frac{L}{6}=x[/tex]
[tex]x=\frac{5L}{6}[/tex]
Therefore another child is sitting at a distance of [tex]\frac{5L}{6}[/tex]
