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
$\frac{{mg \times \pi }}{{2{\theta _o}}}$
$\frac{{mg \times \pi }}{{2\left( {1 - \mu } \right){\theta _o}}}$
$\frac{{mg \times \pi }}{{\left( {1 - \mu } \right)}}$
$\frac{{mg \times \pi }}{{2\left( {1 - \mu } \right)}}$
A block of mass $2 kg$ slides down an incline plane of inclination $30^o$. The coefficient of friction between block and plane is $0.5$. The contact force between block and plank is :
A horizontal force of $10 \,N$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $0.2$. the weight of the block is ........ $N$
......... $m/s^2$ is magnitude of acceleration of a block moving with speed $10\,m/s$ on a rough surface if coefficient of friction is $0.2$.
A pen of mass $m$ is lying on a piece of paper of mass $M$ placed on a rough table. If the coefficients of friction between the pen and paper and the paper and the table are $\mu_1$ and $\mu_2$, respectively. Then, the minimum horizontal force with which the paper has to be pulled for the pen to start slipping is given by
If the normal force is doubled, the coefficient of friction is