A column of rectangular cross-section d units × 1 unit at top is subjected to a load P in addition to its self weight. Then the profile for uniform stress along its length is (ρ = density, σ = stress)

• A. \({\rm{d}}{{\rm{e}}^{\left( {\frac{{{\rm{\rho x}}}}{{\rm{\sigma }}}} \right)}}\)
• B. \({\rm{d}}{{\rm{e}}^{\left( {\frac{{\rm{\sigma }}}{{{\rm{\rho x}}}}} \right)}}\)
• C. \({\rm{d}}{{\rm{e}}^{\left( {\frac{{\rm{x}}}{{\rm{\sigma }}}} \right)}}\)
• D. \({\rm{d}}{{\rm{e}}^{\left( {\frac{{\rm{\rho }}}{{\rm{\sigma }}}} \right)}}\)