The device in Figure $2$ can support a load $\backslash ($ F $\backslash )$ at various heights by re$-$setting the pawl $\backslash ($ P $\backslash )$ in a tooth of the fixed ratchet at the desired height. Neglect weight of the device compared to $\backslash ($ F $\backslash ).($a$)$ Find the reactions at $\backslash ($ A$,$ B $\backslash )$ and $\backslash ($ C $\backslash )$ for $\backslash ($ F$=\backslash )2000$ N$,\backslash ($ d$=100\backslash$mathrm$\{$~mm$\}\backslash ).($b$)$ Find the distance $\backslash ($ d $\backslash )$ of the load $\backslash ($ F $\backslash )$ so that the rollers at $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ support optimum forces. Find the supporting forces for $\backslash ($ F$=2000\backslash )$ N$.$

Figure $2$