An object takes $n$ times as much time as to slide down a $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth inclined plane of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by

• Correct answer
  A

  $\left(1-\frac{1}{n^2}\right)$
• B

  $\left(\frac{1}{1-n^2}\right)$
• C

  $\sqrt{1-\frac{1}{n^2}}$
• D

  $\sqrt{1+\frac{1}{n^2}}$

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