A block of mass $m$ (initially at rest) is sliding up (in vertical direction) against 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 sec. At $t$ = $0$ , the force is in vertical upward direction and then as time passes its direction is getting along normal, i.e., $\theta = \frac{\pi }{2}$ .The value of $F$ so that the block comes to rest when $\theta = \frac{\pi }{2}$ , is
A block of mass $m$ (initially at rest) is sliding up (in vertical direction) against 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 sec. At $t$ = $0$ , the force is in vertical upward direction and then as time passes its direction is getting along normal, i.e., $\theta = \frac{\pi }{2}$ .The value of $F$ so 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
$\frac{{mg \times \pi }}{{2\left( {1 - \mu } \right)}}$
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- [IIT 2004]