Right option is (d) \(c_v=\frac{(T_v)_{50} d^2}{t_{50}} \)
The explanation is: For logarithm of time fitting method, the coefficient of consolidation is detained from,
\(c_v=\frac{(T_v)_{50} d^2}{t_{50}}\)
where, cv=coefficient of consolidation
(Tv)50=time factor corresponding to 50% consolidation
t50=elapsed time for 50% consolidation
d=average drainage path for pressure increment.