A given object takes n times as much time to slide down a\[45{}^\circ \]rough incline as it takes to slide down a perfectly smooth \[45{}^\circ \] incline. The coefficient of kinetic friction between the object and the incline is given by [RPET 1999; AMU 2000]

• A.                         \[\left( 1-\frac{1}{{{n}^{2}}} \right)\]            
• B.                           \[\frac{1}{1-{{n}^{2}}}\]            
• C.                         \[\sqrt{\left( 1-\frac{1}{{{n}^{2}}} \right)}\]            
• D.                           \[\sqrt{\frac{1}{1-{{n}^{2}}}}\]