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 block of mass $m$ is at rest relative to the stationary wedge of mass $M$. The coefficient of friction between block and wedge is $\mu$. The wedge is now pulled horizontally with acceleration $a$ as shown in the figure. Then the minimum magnitude of $a$ for the friction between block and wedge to be zero is

Two blocks $A$ and $B$ are placed on a plane surface as shown in the figure. The mass of block $A$ is $100 \mathrm{kg}$ and that of block $B$ is $200 \mathrm{kg}$. Block $A$ is tied to a stand and block $B$ is pulled by a force $F$. If the coefficient of friction between the surfaces of $A$ and $B$ is $0.2$ and the coefficient of friction between $B$ and the plane is $0.3$, then for the motion of $B$ the minimum value of $F$ will be,