A pulley of radius $2 \mathrm{m}$ is rotated about its axis by a force $=\left(20t-5t^2\right)$ newton (where $t$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is $10 \mathrm{kg} {\mathrm{m}}^2,$ the number of rotation made by the pulley before its direction of motion is reversed is

Two blocks $A$ and $B$ are placed one over the other on a smooth horizontal surface. The maximum horizontal force that can be applied on lower block $A$, so that $A$ and $B$ move without separation is $49 \mathrm{N}$. The coefficient of friction between $A$ and $B$ is

A block $A$ of mass $100 \mathrm{kg}$ rests on another block $B$ of mass $200 \mathrm{kg}$ and is tied to a wall as shown in the figure. The coefficient of friction between $A$ and $B$ is $0.2$ and that between $B$ and ground is $0.3$. The minimum force required to move the block $B$ is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$