Two Block Problems

Block $A$ of mass $m$ and block $B$ of mass $2m$ are placed on a fixed triangular wedge by means of a massless inextensible string and a frictionless pulley as shown in figure. The wedge is inclined at $45°$ to the horizontal on both sides. The coefficient of friction between block $A$ and the wedge is $\frac{2}{3}$ and that between block $B$ and the wedge is $\frac{1}{3}$. If the system of $A$ and $B$ is released from rest, find the acceleration of $A \& B$.

Two blocks connected by a massless string slide down an inclined plane having an angle of inclination of  $37°.$  The masses of the two blocks are  $M_1=4kg$  and  $M_2=2kg$  respectively and the coefficients of friction of  $M_1$ and  $M_2$ with the inclined plane are 0.75 and 0.25 respectively. Assuming the string to the taut, find the tension in the string.  $\left(\sin 37°=0.6,\cos 37°=0.8\right)$

Two blocks connected by a massless string slide down an inclined plane having an angle of inclination of $37°.$ The masses of the two blocks are $M_1=4 \mathrm{kg}$ and $M_2=2 \mathrm{kg}$ respectively and the coefficients of friction of $M_1$ and $M_2$ with the inclined plane are $0.75$ and $0.25$ respectively. Assuming the string to be taut, find the common acceleration of two masses. $\left(\sin 37°=0.6, \cos 37°=0.8\right)$

In the arrangement coefficient of friction between the two blocks is $\mu =\frac{1}{3}$. The force of friction acting between the two blocks is: $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A body B lies on a smooth horizontal table and another body A is placed on B. The coefficient of friction between A and B is $\mu$. What acceleration given to B will cause slipping to occur between A and B

A man sitting in a train in motion is facing the engine. He tosses a coin up, the coin falls behind him. The train is moving

A single horizontal force F is applied to a block of mass $M_1$, which is in contact with another block of mass $M_2$(Given figure). If the surfaces are frictionless, the force between the blocks is

A body is moving down a long inclined plane of $1$ in $2$. The co-efficient of kinetic friction between the body and the plane varies as $\mu =0.49 x$ where $x$ is the distance moved down the plane. The body will have its maximum velocity when it reaches

Two blocks of masses $M=5 \mathrm{kg}$ and $m=3 \mathrm{kg}$ are placed on a horizontal surface as shown in fig. The coefficient of friction between the blocks is $0.5$ and that between the block $M$ and the horizontal surface is $0.7$. What is the maximum horizontal force $F$ that can be applied to block $M$ so that the two blocks move without slipping ? Take $g=10 \mathrm{m}/{\mathrm{s}}^2$

In figure, the coefficient of friction between the floor and the block $B$ is $0.1$. The coefficient of friction between the blocks $B$ and $A$ is $0.2$. The mass of $A$ is $\frac{m}{2}$ and of $B$ is$m$. What is the maximum horizontal force $F$ can be applied to the block $B$ so that two blocks move together?

A block of mass $10 \mathrm{kg}$ is placed on rough horizontal surface whose coefficient of friction is $0.5.$ If a horizontal force of $100\mathrm{ }\mathrm{N}$ is applied on it, then acceleration of the block will be
$(\mathrm{T}\mathrm{a}\mathrm{k}\mathrm{e}\mathrm{ }\mathrm{g}=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2})$

Blocks $A$ and $B$ are arranged as shown in the figure. The pulley is frictionless. The mass of $A$ is $10 \mathrm{kg}$. The coefficient of friction between the block $A$ and the horizontal surface is $0.20$. The minimum mass of $B$, to start the motion, will be

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 $\left[\mathrm{take}, g=10 \mathrm{m} {\mathrm{s}}^{-2}\right]$

A block of mass $m=2 \mathrm{kg}$ is placed on a plank of mass $\mathrm{M}=10 \mathrm{kg},$ which is placed on a smooth horizontal plane, as shown in the figure. The coefficient of friction between the block and the plank is $\mu =\frac{1}{3}.$ If a horizontal force $F$ is applied on the plank, then the maximum value of $F$ for which the block and the plank move together is $\left(\mathrm{g}=10 \mathrm{m}/{\mathrm{s}}^2\right)$

In the arrangement shown in the figure, if the blocks of masses $m$ and $2 \mathrm{m}$ are released from the state of rest, tension in the string is ($\mu =$ coefficient of friction, string is massless and inextensible, pulley is frictionless)

In the situation shown, the reading of the spring balance is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

Block 1 sits on top of block $2$. Both of them have a mass of $1$ $\mathrm{kg}$. The coefficients of friction between blocks $1$ and $2$ are ${\mu }_{\mathrm{s}}=0.75$ and ${\mu }_{\mathrm{k}}=0.60$. The table is frictionless. A force $\frac{P}{2}$ is applied on block $1$ to the left, and force $P$ on block $2$ to the right. Obtain the minimum value of $P=P_{\min }$ such that both blocks move relative to each other and fill $\frac{P_{\min }}{2}$ in OMR.

If $F$ force is applied to $10 \mathrm{kg}$ block as shown in diagram then maximum value of $F$ so that there is no relative motion between the blocks.

Calculate the accelerations of the blocks $A$ and $B:-$

A force of $0.5 \mathrm{N}$ is applied on the upper block as shown in figure. The coefficient of static friction between the two blocks is $0.1$ and that between the lower block and the surface is zero. The work done by the lower block on the upper block for a displacement of $3 \mathrm{m}$ of the upper block is :-