The upper half of an inclined plane with inclination $\varphi$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, if the coefficient of friction for the Lower half is given by
 

• A

  $2\sin \mathrm{\varphi }$

• B

  $2\cos \mathrm{\varphi }$

• C

  $2\tan \mathrm{\varphi }$

• D

  $\tan \mathrm{\varphi }$