Maximum stress that can be applied to a wire which supports an elevator is $\mathrm{\sigma }$ . Mass of elevator is m and it is moved upwards with an acceleration of $\frac{\mathrm{g}}{2}$. Minimum diameter of wire (Neglecting weight of wire) must be

• A

  $\sqrt{\frac{2\mathrm{mg}}{\mathrm{\pi \sigma }}}$

• B

  $\sqrt{\frac{3\mathrm{mg}}{2\mathrm{\pi \sigma }}}$

• C

  $\sqrt{\frac{5\mathrm{mg}}{2\mathrm{\pi \sigma }}}$

• D

  $\sqrt{\frac{6\mathrm{mg}}{\mathrm{\pi \sigma }}}$