A farmer has a problem with rats in their barn and has devised a trap to catch these rats. The trap consists of a uniform rod of mass $0\mathrm{.}94$ kg $,$ and length $L=90\mathrm{.}0cm$ balanced as shown in the figure. Two pieces of wood support the rod, one at its end, and the other $60\mathrm{.}0$ cm from the end. A $100$ g piece of cheese at the other end is used as bait for the rats. A rat can walk along the rod towards the cheese eventually it will cause the rod to tip over and drop the rat into the bucket. If the rat is $0\mathrm{.}61$ kg $,$ how far past the $2$ nd support does the rat have to go to tip the rod over and fall into the bucket?