Let 𝐺 be a compact Lie group. In 1960, P A Smith asked the following question: ``Is it true that for any smooth action of 𝐺 on a homotopy sphere with exactly two fixed points, the tangent 𝐺-modules at these two points are isomorphic?" A result due to Atiyah and Bott proves that the answer is `yes’ for $\mathbb{Z}_p$ and it is also known to be the same for connected Lie groups. In this work, we prove that two linear torus actions on $S^n$ which are 𝑐-cobordant (cobordism in which inclusion of each boundary component induces isomorphisms in $\mathbb{Z}$-cohomology) must be linearly equivalent. As a corollary, for connected case, we prove a variant of Smith’s question.