A 900 kg elevator hangs by a steel cable for which the allowable stress is $1.15\times {10}^8\mathrm{N}/{\mathrm{m}}^2$. What is the minimum diameter required if the elevator accelerates upward at $1.5\mathrm{m}/{\mathrm{s}}^2$. Take $g=10\mathrm{m}/{\mathrm{s}}^2$

• A

  $\frac{6\times {10}^{-2}}{\sqrt{5\mathrm{\pi }}}\mathrm{m}$

• B

  $\frac{6\times {10}^{-2}}{\sqrt{10\mathrm{\pi }}}\mathrm{m}$

• C

  $\frac{3\times {10}^{-2}}{\sqrt{10\mathrm{\pi }}}\mathrm{m}$

• D

  $\frac{3\times {10}^{-2}}{\sqrt{5\mathrm{\pi }}}\mathrm{m}$