A block of mass M slides down a rough inclined surface of inclination '$\mathrm{\theta }$‘ and reaches the bottom at speed ’v'. However, if it slides down a smooth inclined surface of same length and same inclination, it reaches the bottom with speed kv. Coefficient of friction between the block and the rough incline is:

• A

  $\sin \mathrm{\theta }\left({\mathrm{k}}^2-1\right)$

• B

  $\left(\frac{{\mathrm{k}}^2-1}{{\mathrm{k}}^2}\right)\tan \mathrm{\theta }$

• C

  $\left(\frac{{\mathrm{k}}^2+1}{{\mathrm{k}}^2}\right)\cos \mathrm{\theta }$

• D

  $\frac{{\mathrm{k}}^2-1}{{\mathrm{k}}^2}$