A horizontal force $12 \,N$ pushes a block weighing $1/2\, kg$ against a vertical wall.  The  coefficient of static friction between the wall and the block is $0.5$ and the coefficient of  kinetic friction is $0.35.$ Assuming that the block is not moving  initially. Which one of the following choices is correct (Take $g = 10 \,m/s^2$)

The frictional force acting on $1 \,kg$ block is .................. $N$

Figure shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with $1\; m s^{-2}$. What is the net force on the man? If the coefficient of static friction between the man’s shoes and the belt is $0.2$, up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man $= 65 \;kg.)$

In the figure, a ladder of mass $m$ is shown leaning against a wall. It is in static equilibrium making an angle $\theta$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $\mu_1$ and that between the floor and the ladder is $\mu_2$. The normal reaction of the wall on the ladder is $N_1$ and that of the floor is $N_2$. If the ladder is about to slip, then

$Image$

$(A)$ $\mu_1=0 \mu_2 \neq 0$ and $N _2 \tan \theta=\frac{ mg }{2}$

$(B)$ $\mu_1 \neq 0 \mu_2=0$ and $N_1 \tan \theta=\frac{m g}{2}$

$(C)$ $\mu_1 \neq 0 \mu_2 \neq 0$ and $N _2 \tan \theta=\frac{ mg }{1+\mu_1 \mu_2}$

$(D)$ $\mu_1=0 \mu_2 \neq 0$ and $N _1 \tan \theta=\frac{ mg }{2}$

A block of mass $2 \,kg$ is kept on the floor. The coefficient of static friction is $0.4$. If a force F of $2.5$ Newtons is applied on the block as shown in the figure, the frictional force between the block and the floor will be ........ $N$ 

A block of mass $1\, kg$ is at rest on a horizontal table. The coefficient of static friction  between the block and the table is $0.5.$ The magnitude of the force acting upwards at  an angle of $60^o$ from the horizontal that will just start the block moving is