The Young's modulus of a rubber string 8 cm long and density  $1.5\mathrm{kg}/{\mathrm{m}}^3$ is $5\times {10}^8\mathrm{N}/{\mathrm{m}}^2$ , is suspended on the ceiling in a room. The increase in length due to its own weight will be 

• A

  $9.6\times {10}^{-5}\mathrm{m}$

• B

  $9.6\times {10}^{-11}\mathrm{m}$

• C

  $9.6\times {10}^{-3}\mathrm{m}$

• D

  $9.6 \mathrm{m}$