Two-Block Problems

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. $\left(\sin 37°=0.6, \cos 37°=0.8\right)$

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 $g=10 \mathrm{m}/{\mathrm{s}}^2$

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 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 $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

The system is pushed by the force $F$ as shown. All surfaces are smooth except between $B$ and $C$. Friction coefficient between $B$ and $C$ is $\mu .$ Minimum value of $F$ to prevent block $B$ from downward slipping is

Two blocks are placed on a wedge with coefficients of friction being different for two blocks. Choose the correct option. (friction is not sufficient to prevent the motion)

Two blocks of mass $6 \mathrm{kg}$ and $4 \mathrm{kg}$ are pushed along a horizontal frictionless surface by a force of $40 \mathrm{N}$ applied to the $6 \mathrm{kg}$ block at an angle of $60°$ to the horizontal. The force that the $4 \mathrm{kg}$ block exerts on the $6 \mathrm{kg}$ block is

If acceleration of $A$ is $2 \mathrm{m}/{\mathrm{s}}^2$ which is smaller than acceleration of $B$ then the value of frictional force applied by $B$ on $A$ is :

The friction coefficient between the table and the block shown in figure is $0.2$. Find the tension in the string which is connected with both $5 \mathrm{kg}$ blocks.

coefficient of friction between two blocks $A$ and $B$ of masses $4 \mathrm{kg}$ and $2 \mathrm{kg}$ respectively is $\mu =0.5$ and horizontal floor is frictionless as shown in the given figure. If $A$ is pulled to right by $24 \mathrm{N}$ through $10 \mathrm{m},$ then work done by the force of friction on $B$ is

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.

Initially the whole system is at rest and now a force of $62 \mathrm{N}$ is applied on the block '$B$' as shown in the figure. Find the time taken by '$A$' (in $\sec$) to fall from the block '$B$' :-

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 $B:-$

The friction coefficient between the blocks is $0.5.$ The acceleration of each block is :-

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 :-

In friction is present between $A \text{\&} B$ only and $F>$ limiting friction between $A\text{ \&} B$. Find acceleration of $A \text{\&} B\mathit{.}$