An organic compound $P$ with molecular formula $C _9 H _{18} O _2$ decolorizes bromine water and also shows positive iodoform test. $P$ on ozonolysis followed by treatment with $H _2 O _2$ gives $Q$ and $R$. While compound $Q$ shows positive iodoform test, compound $R$ does not give positive iodoform test. $Q$ and $R$ on oxidation with pyridinium chlorochromate ($PCC$) followed by heating give $S$ and $T$, respectively. Both $S$ and $T$ show positive iodoform test.
Complete copolymerization of 500 moles of $Q$ and $500$ moles of $R$ gives one mole of a single acyclic copolymer $U$.
[Given, atomic mass: $H=1, C=12, O=16$ ]
($1$) Sum of number of oxygen atoms in $S$ and $T$ is. . . . . .
($2$) The molecular weight of $U$ is
Give the answer or quetion $(1)$ and $(2)$