A girl holds a book of mass $m$ against a vertical wall with a horizontal force $F$ using her finger, so that the book does not move. The frictional force on the book by the wall is

A circular racetrack of radius $300\; m$ is banked at an angle of $15^o$. If the coefficient of friction between the wheels of a race-car and the road is $0.2$, what is the

$(a)$ optimum speed of the racecar to avoid wear and tear on its tyres, and

$(b)$ maximum permissible speed to avoid slipping ?

As shown in the figure a block of mass $10\,kg$ lying on a horizontal surface is pulled by a force $F$ acting at an angle $30^{\circ}$, with horizontal. For $\mu_{ s }=0.25$, the block will just start to move for the value of $F..........\,N$ : $\left[\right.$ Given $\left.g =10\,ms ^{-2}\right]$

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 

Someone is using a scissors to cut a wire of circular cross section and negligible weight. The wire slides in the direction away from the hinge until the angle between the scissors blades becomes $2 \alpha$. The friction coefficient between the blades and the wire, is :-

Maximum value of static friction is called