The upper half of an inclined plane with inclination $\mathrm{\varphi }$ 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 coefficient of friction for the lower half is given by:

• A

  $2\tan \mathrm{\varphi }$

• B

  $\tan \mathrm{\varphi }$

• C

  $2\sin \mathrm{\varphi }$

• D

  $2\cos \mathrm{\varphi }$