A wooden block of mass $m$ resting on a rough horizontal table (coefficient of friction = $\mathrm{\mu }$) is pulled by a force $F$ as shown in the figure. The acceleration of the block moving horizontally is:

 

Two blocks $m_1=4 \mathrm{kg}$ and $m_2=2 \mathrm{kg}$, connected by a weightless rod on a plane having inclination of $37°$ as shown in the figure. The coefficients of dynamic friction of $m_1$ and $m_2$ with the inclined plane is $\mathrm{\mu }=0.25$. Then the common acceleration of the two blocks and the tension in the rod are: (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A cart of mass $M$ has a block of mass $m$ attached to it as shown in the figure. Co-efficient of friction between the block and cart is $\mu$. What is the minimum acceleration of the cart so that the block m does not fall?

Two masses $A$ and $B$ of $10 \mathrm{kg}$ and $5 \mathrm{kg}$ respectively are connected with a string passing over a frictionless pulley fixed at the corner of a table as shown. The coefficient of static friction of $A$ with table is $0.2$. The minimum mass of $C$ that may be placed on $A$ to prevent it from moving is

A force $F=t$ is applied to block $A$ as shown in the figure. The force is applied at $t=0 \mathrm{s}$ when the system was at rest and the string is just straight without tension. Which of the following graphs gives the friction force between $B$ and horizontal surface as a function of time $t$?