A lift is tied with thick iron ropes having mass 'M'. The maximum acceleration of the lift is 'a' $\mathrm{m} / \mathrm{s}^{2}$ and maximum safe stress is 's' $\mathrm{N} / \mathrm{m}^{2}$. The minimum diameter of the rope is ( $\mathrm{g}=$ acceleration due to gravity $)$

• A

  $\left[\frac{2 \mathrm{M}(\mathrm{g}+\mathrm{a})}{\pi \mathrm{s}}\right]^{\frac{1}{2}}$
• B

  $\left[\frac{2 \mathrm{M}(\mathrm{g}-\mathrm{a})}{\pi \mathrm{s}}\right]^{\frac{1}{2}}$
• Correct answer
  C

  $\left[\frac{4 \mathrm{M}(\mathrm{g}+\mathrm{a})}{\pi \mathrm{s}}\right] \overline{\frac{1}{2}}$
• D

  $\left[\frac{4 \mathrm{M}(\mathrm{g}-\mathrm{a})}{\pi \mathrm{s}}\right] \frac{1}{2}$

Hence, the correct answer is option: 'C'.