Static Friction

Consider a car moving along a straight horizontal road with speed of $72 \mathrm{km} {\mathrm{hr}}^{-1}$  . If the coefficient of static friction between the tyres and the road is $0.5$, the shortest distance in which the car can be stopped is  (taking $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The coefficient of static friction, ${\mu }_s,$  between block $A$ of mass $2 \mathrm{kg}$ and the table as shown in the figure is $0.2$. The maximum mass value of block $B$ so that the two blocks do not move is (The string and the pulley are assumed to be smooth and massless $g=10 \mathrm{m} {\mathrm{s}}^{-2})$

A block of mass $2 \mathrm{kg}$ rests on a rough inclined plane making an angle of $30º$ with the horizontal. The coefficient of static friction between the block and the plane is $0.7.$ The frictional force on the block is

An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is $\frac{1}{3}$. If the line joining the center of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is given by,

A block of mass $1 \mathrm{kg}$ lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is $0.6$. If the acceleration of the truck is $5\mathrm{m}{\mathrm{s}}^{-2}$. Find the frictional force acting on the block.

A block $A$ with mass $100 \mathrm{kg}$ is resting on another block $B$ of mass $200 \mathrm{kg}.$ As shown in figure, a horizontal rope tied to a wall holds it. The coefficient of friction between $A$ and $B$ is $0.2$ while coefficient of friction between $B$ and the ground is $0.3.$The minimum required force $F$ to start moving $B$ will be

Consider the situation shown in the figure. The wall is smooth but the surfaces of blocks $\text{A}$ and $\text{B}$ in contact are rough. The friction on $\text{A}$ due to $\text{B}$ in equilibrium

Consider the system shown in the figure. The wall is smooth, but the surfaces of blocks $A$ and $B$ in contact are rough. The friction on $B$ due to $A$ in equilibrium is

In the given diagram, what is the minimum value of horizontal external force $F$ on block $A$ so that block $B$ slides on the ground?

A block of mass$m$ is at rest relative to a stationary wedge of mass $M$. The coefficient of friction between the block and the wedge is $\mathit{\text{μ}}$. The wedge is now pulled horizontally with an acceleration $a$, as shown in the figure. Then, the minimum magnitude of $a$ for the friction between the block and the wedge to be zero, is

A force $F=5 \mathrm{N}$ is applied on the lower block as shown in figure. The work done by lower block on upper block for a displacement of $6 \mathrm{m}$ of the upper block with respect to ground is $\left[\mathrm{take}, g=10 \mathrm{m} {\mathrm{s}}^{-2}\right]$

Two blocks $A \left(1\mathrm{ }\mathrm{kg}\right)$ and $B\mathrm{ }\left(2\mathrm{ }\mathrm{kg}\right)$ are connected by a string passing over a smooth pulley as shown in the figure. $B$ rests on a rough horizontal surface and $A$ rests on $B$. The coefficient of friction between $A$ and $B$ is the same as that between $B$ and the horizontal surface. The minimum horizontal force $F$ required to move $A$ to the left is $25\mathrm{ }\mathrm{N}.$ The coefficient of friction is $\mu$. The value of $\mu$ is $\frac{1}{x}$. The value of $x$ will be $(g=10\mathrm{ }\mathrm{m} {{\mathrm{s}}^{-}}^2)\mathrm{ }$

Three blocks are kept as shown in figure. Acceleration of $20 \mathrm{kg}$ block with respect to ground in $\mathrm{SI}$ unit is.

The magnitude of frictional force acting between the block and the inclined plane, as shown in the figure, is (take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

One-fourth length of a uniform rod is placed on a rough horizontal surface and it starts rotating about the edge as soon as we release it. The rod starts slipping on the edge when it has turned through an angle $\theta$. If the coefficient of friction between rod and surface is $\mu$, and it satisfies the relation $x\tan \theta =4\mu$, then what is the value of $x$?

[Take $g=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$]

For a truck with $14$ tyres, only rear $8$ wheels are power driven and can produce acceleration. These $8$ wheels support half the entire load. If the coefficient of friction between road and each tyre is $0.6$, the maximum attainable acceleration by this truck would be (Acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Sand is to be piled up on a horizontal ground in the form of a regular cone of a fixed base of radius $R$. Coefficient of static friction between the sand layers is $\mu$. Maximum volume of the sand that can be piled up in the form of cone without slipping on the ground is

A block of mass $1 \mathrm{kg}$ lies on a horizontal surface in a truck. The coefficient of static friction between the block and the surface is $0.6$. If the acceleration of the truck is $5 {\mathrm{ms}}^{-2}$ The frictional force acting on the block is: