If the coefficient of friction between $A$ and $B$ is ${\mu }_1$ the maximum horizontal acceleration of the wedge $A$ for which $B$ will remain at rest with respect to the wedge is:

What is the minimum stopping distance for a vehicle of mass $m$ moving with speed $v$ along a level road if the coefficient of friction between the tyres and the road is $\mu$?

A block of mass $m_1=1 \mathrm{kg}$ another mass $m_2=2 \mathrm{kg}$ are placed together (see figure) on an inclined plane with the angle of inclination $\mathrm{\theta }.$ Various values $\mathrm{\theta }$ are given in List $\mathrm{I}.$ The coefficient of friction between the block $m_1$ and the plane is always zero. The coefficient of static and dynamic friction between the block $m_2$ and the plane is equal to$\mu =0.3$. In List$\mathrm{ll}$, an expression for the friction on block $m_2$ given. Match the correct expression of the friction in List $\mathrm{II}$ with the angles given in List $1$ and choose the correct option. The acceleration due to gravity is denoted by $g$ [useful information: $\tan \left(5.5°\right)\approx 0.1; \tan \left(11.5°\right)\approx 0.2; \tan \left(16.5°\approx 0.3\right)]$

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Assertion: While drawing a line on a paper, friction force acts on paper in the same direction along which line is drawn on the paper.

Reason: Friction always opposes motion.

Assertion: A man and a block rest on smooth horizontal surface. The man holds a rope which is connected to block. The man cannot move on the horizontal surface.

Reason: A man standing at rest on smooth horizontal surface can start walking due to absence of friction (the man is only in contact with floor as shown).

Assertion : A block of mass $\mathrm{m} \mathrm{kg}$ is kept on rough fixed horizontal surface as shown. The coefficient of friction between block and horizontal surface is $\mu =0.1$. Then the magnitude of minimum horizontal force required to move the block is $\mathrm{m}$ Newton (Take $\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2$ )

Reason : A block is kept on fixed rough horizontal surface. The limiting value of friction force is given by $\mu \mathrm{N}$, where $\mu$ is coefficient of kinetic friction (between the block and the horizontal surface) and $\mathrm{N}$ is normal reaction on block due to horizontal surface.

A block of mass $m$ is in contact with the cart $C$ as shown in the figure.

The coefficient of static friction between the block and the cart is $\mu$. The acceleration $\alpha$ of the cart that will prevent the block from failing satisfies the equation,