A bullet of mass $4\,g$ is fired horizontally with a speed of $300\,m/s$ into $0.8\,kg$ block of wood at rest on a table. If the coefficient of friction between the block and the table is $0.3,$ how far will the block slide approximately?

Given in the figure are two blocks $A$ and $B$ of weight $20\, N$ and $100\, N$, respectively. These are being pressed against a wall by a force $F$ such that the system does not slide as shown. If the coefficient of friction between the blocks is $0.1$ and between block $B$ and the wall is $0.15$, the frictional force applied by the wall on block $B$ is ........ $N$

A block is moving on an inclined plane making an angle $45^{\circ}$ with the horizontal and the coefficient of friction is $\mu$. The force required to just push it up the inclined plane is $3$ times the force required to just prevent it from sliding down. If we define $N=10 \ \mu$, then $N$ is

Static friction between two surfaces

The rear side of a truck is open and a box of $40 \;kg$ mass is placed $5 \,m$ away from the open end as shown in Figure. The coeffictent of friction between the box and the surface below it is $0.15 .$ On a stratght road, the truck starts from rest and accelerates with $2\; m s ^{-2} .$ At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).

A vehicle is moving with speed $v$ on a curved road of radius $r$. The coefficient of friction between the vehicle and the road is $\mu$. The angle $\theta$ of banking needed is given by