Two masses $m_1=4 \mathrm{kg}$ and $m_2=2 \mathrm{kg}$ are connected with an inextensible, massless string that passes over a frictionless pulley and through a slit, as shown. The string is vertical
on both sides and the string on the left is acted upon by a constant function force $10 \mathrm{N}$ by the slit as it moves. Then

In the arrangement, as shown, the block $A$ of mass $3 \mathrm{kg}$ moves towards the left with velocity $10 \mathrm{m} {\mathrm{s}}^{-2}$. Initially, the block $A$ is $100 \mathrm{m}$ from a pulley on a smooth surface. Block $B$ is of mass $2 \mathrm{kg}$

A triangular prism of mass $M$ with a block of mass $m$ placed on it is released from rest on a smooth inclined plane of inclination $\theta$. The block does not slip on the prism. Then

Block $B$, of mass $m_{\mathrm{B}}=0.5 \mathrm{kg}$, rests on the block $A$, with mass $m_{\mathrm{A}}=1.5 \mathrm{kg}$, which in turn is on a horizontal tabletop (as shown in the figure). The coefficient of kinetic friction between the block $A$ and the tabletop is ${\mu }_{\mathrm{k}}=0.4$ and the coefficient of static friction between block $A$ and block $B$ is ${\mu }_{\mathrm{s}}=0.6$. A light string attached to the block $A$ passes over a frictionless, massless pulley and the block $C$ is suspended from the other end of the string. What is the largest mass $m_{\mathrm{C}}$ (in $\mathrm{kg}$) that block $C$ can have so that blocks $A$ and $B$ still slide together when the system is released from rest?

A block of mass $m=2 \mathrm{kg}$ is resting on a rough inclined plane of inclination $30°$ as shown in the figure. The coefficient of friction between the block and the plane is $\mu =0.5$. What minimum force $F$ (in newton) should be applied perpendicular to the plane on the block so that the block does not slip on the plane?

A block $A$ of mass $m$ is placed over a plank $B$ of mass $2m.$ Plank $B$ is placed over a smooth horizontal surface. The coefficient of friction between $A$ and $B$ is $0.4$. Block $A$ is given a velocity towards the right. Find acceleration (in $\mathrm{m} {\mathrm{s}}^{-2}$) of $B$ relative to $A.$

A blocks $A,$ of weight $W,$ slides down an inclined plane $S$ of slope $37°$at a constant velocity, while the plank $B,$ also of weight $W,$ rests on top $A.$ The plank $B$ is attached by a cord to the top of the plane. The coefficient of kinetic friction $\mu$ is the same between the surfaces $A$ and $B$ and between $S$ and $A.$ Determine the value of $\frac{1}{\mu }.$

A chain of mass $10 \mathrm{kg}$ and length $8 \mathrm{m}$ is resting on a rough horizontal surface $\left(\mu =0.2\right).$ A force $F = 15 \mathrm{N}$ is applied as shown. Find the length (in $m$) of the chain on which no friction force acts.

A $10 \mathrm{kg}$ block is resting on the horizontal surface when the force $F$ is applied to it for $7$ seconds. The variation of $F$ with time is shown. The coefficients of static and kinetic friction are both $0.50.$ Find the velocity of the block (in $\mathrm{m} {\mathrm{s}}^{-1}$) at $t=4 \sec .$