A sphere of radius r and density p is dropped under gravity through a fluid of viscosity $\mathrm{\eta }$. If the average acceleration is half of initial acceleration, what is the time required to attain terminal velocity? (Neglect buoyant force) 

• A

  $\frac{4{\mathrm{\rho r}}^2}{\left(9\mathrm{\eta }\right)}$

• B

  $\frac{9{\mathrm{\rho r}}^2}{\left(4\mathrm{\eta }\right)}$

• C

  $\frac{4{\mathrm{\rho r}}^2}{\left(3\mathrm{\eta }\right)}$

• D

  $\frac{{\mathrm{\rho r}}^2}{\mathrm{\eta }}$