Problem $2$: Using a series of levers is more efficient than using a single lever. For example, the $6-Mg$ truck is balanced on a scale using either $($a$)$ three levers or $($b$)$ one lever as shown. In case $($a$),$ determine the force $P$ required for equilibrium of the truck, and in case $($b$),$ using the same force $P,$ determine the length $1$ of the single lever necessary for balancing the truck.