Two $30-\mathrm{kg}$ blocks rest on a massless belt which passes over a fixed pulley and is attached to a $40 \mathrm{kg}$ block. If coefficient of friction between the belt and the table as well as between the belt and the blocks $B$ and $C$ is $\mu$ and the system is released from rest from the position shown, the speed with which the block $B$ falls off the belt is 

A $10 \mathrm{kg}$ block is at rest as shown on the horizontal surface having a coefficient of static friction of $0.7$. String-$1$ is horizontal and string-$2$ makes an angle of $30°$ with the vertical. A mass $M$ hangs from string-$3$. Which of the following statement(s) about this situation is/are true? $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A box is accelerating with acceleration $=20 \mathrm{m} {\mathrm{s}}^{-2}$. A block of mass $10 \mathrm{kg}$ placed inside the box and is in contact with the vertical wall as shown. The friction coefficient between the block and the wall is $\mu =0.6$ and take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$. 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 $A.$