Question

prove that this equation is dimensionally true
escape velocity = (2*GM/R) ^1/2

Answer 1

Dear Student,


$$\begin{gathered} v=\sqrt{\frac{2GM}{R}} \\ dimensionofv=\left[L{T}^{-1}\right] \\ G=\left[M^{-1}{L}^3{T}^{-2}\right] \\ M=\left[M\right] \\ R=\left[L\right] \\ fromhomogeneity \\ \frac{{\left[M^{-1}{L}^3{T}^{-2}\right]}^{1/2}{\left[M\right]}^{1/2}}{\left[L^{1/2}\right]}=\left[L{T}^{-1}\right]henceproved \\ Regards \end{gathered}$$