Kykk�nen, AnttiAnttiKykk�nenMishra, Rohit KumarRohit KumarMishraSahoo, Suman KumarSuman KumarSahoo2026-03-062026-03-062026-02-0110.48550/arXiv.2602.18983https://repository.iitgn.ac.in/handle/IITG2025/34783We study a solenoidal-potential type decomposition of a symmetric m-tensor field in \Rb^2, and its implications to injectivity questions for the momentum and elastic ray transforms. For symmetric tensor fields, a general decomposition with a restriction on the dimension and order of the decomposition was proved in~\cite{Rohit_Suman}. We extend the result to dimension 2 under a mean-zero assumption. We use the decomposition in 2 dimensions to prove the injectivity of the momentum and elastic ray transforms. We also prove a connection between the two integral transforms for 2-tensors.en-USe-Print