$A$ block of mass $m$ (initially at rest) is sliding up a rough vertical wall with the help of a force $F$ whose magnitude is constant but direction is changing. $\theta = {\theta _0}t$,where $t$ is time in seconds. At $t = 0$,the force is in the vertical upward direction,and as time passes,its direction changes until $\theta = \frac{\pi }{2}$. The value of $F$ such that the block comes to rest when $\theta = \frac{\pi }{2}$ is:

• A
  $\frac{{mg \times \pi }}{{2{\theta _o}}}$
• B
  $\frac{{mg \times \pi }}{{2\left( {1 - \mu } \right){\theta _o}}}$
• C
  $\frac{{mg \times \pi }}{{\left( {1 - \mu } \right)}}$
• D
  $\frac{{mg \times \pi }}{{2\left( {1 - \mu } \right)}}$